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| In [[commutative algebra]] and [[algebraic geometry]], the '''localization''' is a formal way to introduce the "denominators" to given a ring or a module. That is, it introduces a new ring/module out of an existing one so that it consists of [[algebraic fraction|fractions]]
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| :<math>\frac{m}{s}</math>.
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| where the [[denominator]]s ''s'' range in a given subset ''S'' of ''R''. The basic example is the construction of the ring '''Q''' of rational numbers from the ring '''Z''' of rational integers.
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| The technique has become fundamental, particularly in [[algebraic geometry]], as it provides a natural link to [[sheaf (mathematics)|sheaf]] theory. In fact, the term ''localization'' originates in [[algebraic geometry]]: if ''R'' is a ring of [[function (mathematics)|function]]s defined on some geometric object ([[algebraic variety]]) ''V'', and one wants to study this variety "locally" near a point ''p'', then one considers the set ''S'' of all functions which are not zero at ''p'' and localizes ''R'' with respect to ''S''. The resulting ring ''R*'' contains only information about the behavior of ''V'' near ''p''. Cf. the example given at [[local ring]].
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| <!-- Somehow this paragraph is cryptic to me. Is this really important/helpful? -- Taku | | The London schedule has long had cheerleaders for its talent on home territory, but in the past it has been squeezed out by more commercially robust cities.<br><br>Now it seems the capital is holding its ground against the bigger boys, as more and more international press, and buyers, make London an important stop in their schedule - blizzards in New York notwithstanding.<br>This in part has been due to brands like Burberry Prorsum, Mulberry and Tom Ford, which, with the weight of their advertising budgets behind them, command an international audience. Topshop, led by creative director Kate Phelan, also of British Vogue, has also helped provide financial support and a professional framework in which the creativity of London�s emerging designers can be showcased.<br><br>This situation has not gone unnoticed in Milan, where Giorgio Armani has taken Stella Jean under his wing, hosting her spring/summer 2014 show last September. �The new generation of Italian designers needs our support,� said Armani, echoing the sentiment that has long made London great<br> |
| In [[number theory]] and [[algebraic topology]], one refers to the behavior of a ring or space ''at'' a number ''n'' or ''away'' from ''n''. "Away from ''n''" means "in a ring where ''n'' is invertible" (so a '''Z'''[1/n]-algebra). For instance, for a field, "away from ''p''" means "characteristic not equal to ''p''". '''Z'''[1/2] is "away from 2", but '''F'''<sub>2</sub> or '''Z''' are not.-->
| | LVMH (the parent company of brands such as Louis Vuitton, Christian Dior and [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine Bags Outlet]) is also taking lessons from London: on Thursday it announced a shortlist of 30 designers for its inaugural LVMH Young Fashion Designer Prize. With �300,000 (�246,000) at stake, plus a year of mentoring, the number of London designers shortlisted, including Simone Rocha, Thomas Tait, Meadham Kirchhoff and J JS Lee, is a clear indication of the capital�s fertile groun<br><br> |
| An important related process is [[Completion (ring theory)|completion]]: one often localizes a ring/module, then completes.
| | Fittingly, the nominees - many of which have come through support programmes Newgen and Fashion East - are some of the most exciting shows on the schedul<br> |
| | Korean-born J JS Lee, who trained at Central Saint Martins, took the prized opening slot yesterday in rain-swept central London. For autumn/winter 2014 she showed an elegant collection of brushed mohair, plaid overcoats and formal dresses - experimenting with cocoon shapes, biker jackets and rounded shoulders for the former, while playing with different lengths for the latte<br><br> |
| | Cobalt blue houndstooth as a laser-cut detail and d�grad� printed silk provided a jolt of colour in a predominantly cream, navy and forest-green palette. Slim, long-line trousers were an elegant proposition for evenings, while chunky, cable knits were covetably co<br>. |
| | The London [http://Pinterest.com/search/pins/?q=College College] of Fashion MA Show at the Waldorf Astoria Hotel on day one of London Fashion Week yesterday (PA) With a fit-to-burst schedule of shows, presentations and parties over the next four days, there�s plenty to inspire and excite the fashion world - both on and off the catwa<br><br> |
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| In this article, a ring is commutative with unity.
| | JW Anderson�s first womenswear collection since LVMH bought a minority stake in his business last September is sure to be as controversial as ever: the designer�s gender-blurring take on dressing has its detractors, but just as many fans. The designer was also appointed creative director of Loewe, a Spanish leather brand within the stable, so an excellent accessories offering is to be expect<br><br> |
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| == Construction ==
| | It was all change at Mulberry last season too, as Emma Hill departed after five years as creative director of the [http://www.tumblr.com/tagged/British British] brand. Hill seemed to have hit on a winning formula: balancing design and the right kind of celebrity endorsements fortified the brand�s finances, but recent profit warnings are cited as the reason for her departu<br><br> |
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| === Localization of a ring ===
| | This season, the brand will not be hosting its usual catwalk extravaganza in Claridge�s ballroom. Instead it has announced a photocall at which Cara Delevingne, its campaign face, will reveal the brand�s next big move. Speculation is rife that she will be announced as creative director, but the brand�s success with bags named after It girls makes the debut of the �Cara� a far more likely prosp<br><br> |
| Given a ring ''R'' and a subset ''S'', one wants to construct some ring ''R*'' and [[ring homomorphism]] from ''R'' to ''R*'', such that the image of ''S'' consists of ''[[Unit (ring theory)|units]]'' (invertible elements) in ''R*''. Further one wants ''R*'' to be the 'best possible' or 'most general' way to do this – in the usual fashion this should be expressed by a [[universal property]].
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| Let ''S'' be a [[multiplicatively closed subset]] of a ring ''R'', i.e. for any ''s'' and ''t'' ∈ ''S'', the product ''st'' is also in ''S'', and <math>0 \not\in S</math> and <math>1 \in S</math>. Then the '''localization of ''R'' with respect to ''S''''', denoted ''S''<sup>−1</sup>''R'', is defined to be the following ring: as a set, it consists of [[equivalence relation|equivalence classes]] of pairs (''m'', ''s''), where ''m'' ∈ ''R'' and ''s'' ∈ ''S''. Two such pairs (''m'', ''s'') and (''n'', ''t'') are considered equivalent if there is a third element ''u'' of ''S'' such that
| | Joseph, celebrating 25 years since its first west London boutique opened, is presenting on schedule for the first time too. It may not have the budgets of its blockbuster digital rivals, but it is held in esteem by serious shoppers and the fashion cr<br><br><br> |
| :''u''(''sn''-''tm'') = 0
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| (The presence of ''u'' is crucial to the transitivity of ~) It is common to denote these equivalence classes
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| :<math>\frac{m}{s}</math>.
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| Thus, ''S'' consists of "denominators".
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| To make this set a ring, define
| | While there is a respectable coterie of British luxury brands, it�s the commercial pull of the high street that is unrivalled, something the British Fashion Council - responsible for co-ordinating the schedule - has cottoned on to. As well as Topshop�s premium offering Unique, now a regular on the schedule, the BFC has courted brands such as River Island, which debuted its collaboration with Rihanna in London this time last y<br>r. |
| :<math>\frac{m}{s} + \frac{n}{t} := \frac{tm+sn}{st}</math>
| | Now Whistles is presenting on the schedule for autumn/winter 2014; with a mens collection rumoured to be on the horizon and a flagship store on Mayfair�s Dover Street, the brand is certainly looking to exp<br><br> |
| and
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| :<math>\frac{m}{s} \frac{n}{t} := \frac{m n}{s t}</math>
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| It is straightforward to check that the definition is well-defined, i.e. independent of choices of representatives of fractions. One then checks that the two operations are in fact addition and multiplication (associativity, etc) and that they are compatible (that is, distribution law). This step is also straightforward. The zero element is <math>0/1</math> and the unity is <math>1/1</math>; they are usually simply denoted by ''0'' and ''1''.
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| Finally, there is a canonical map <math>j: R \to S^{-1}R, m \mapsto m/1</math>. (In general, it is not injective; if two elements of ''R'' differ by a nonzero zero-divisor with an annihilator in ''S'', they have the same image by very definition.) The above mentioned universal property is the following: ''j'' : ''R'' → ''R*'' maps every element of ''S'' to a unit in ''R*'' (since (1/s)(s/1) = 1), and if ''f'' : ''R'' → ''T'' is some other ring homomorphism which maps every element of ''S'' to a unit in ''T'', then there exists a unique ring homomorphism ''g'' : ''R*'' → ''T'' such that ''f'' = ''g ○ j''
| | So too are Christopher Kane and Roksanda Ilincic, who plan to open boutiques on Mount Street this year. |
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| If ''R'' has no nonzero zero-divisors (i.e., ''R'' is an integral domain), then the equivalence (''m'', ''s'') ~ (''n'', ''t'') reduces to
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| :''sn'' = ''tm''
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| which is precisely the condition we get when we formally clear out the denominators in <math>\frac{m}{s} = \frac{n}{t}</math>. This motivates the definition above. In fact, the localization recovers the construction of the [[field of fractions]] as follows. Since the zero ideal is prime, its complement ''S'' is multiplicatively closed. The localization <math>S^{-1} R</math> then consists of <math>r/s, r \in R, s \in R^\times</math>. That is, <math>S^{-1} R</math> is precisely the field of fractions ''K'' of ''R''. Since there is no nonzero zero-divisor, the canonical map <math>m \to m/1</math> is an inclusion and one can view ''R'' as a subring of ''K''. Indeed, any localization of an integral domain is a subring of the field of fractions (cf. [[overring]]).
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| If ''S'' equals the complement of a [[prime ideal]] ''p'' ⊂ ''R'' (which is multiplicatively closed by definition of prime ideals), then the localization is denoted ''R''<sub>''p''</sub>. If ''S'' consists of all powers of a nonzero nilpotent ''f'', then <math>S^{-1}R</math>is denoted by either <math>R_f</math> or <math>R[f^{-1}].</math>
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| Another way to describe the localization of a ring ''R'' at a subset ''S'' is via [[category theory]]. If ''R'' is a [[ring (mathematics)|ring]] and ''S'' is a subset, consider the set of all ''R''-algebras ''A'', so that, under the canonical homomorphism ''R'' → ''A'', every element of ''S'' is mapped to a ''unit''. The elements of this set form the objects of a [[category (mathematics)|category]], with ''R''-algebra homomorphisms as morphisms. Then, the localization of ''R'' at ''S'' is the [[initial object]] of this category.
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| === Localization of a module ===
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| The construction above applies to a module <math>M</math> over a ring <math>R</math> except that instead of multiplication we define the scalar multiplication by
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| :<math>a \cdot \frac{m}{s} := \frac{a m}{s}</math>
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| Then <math>S^{-1} M</math> is a <math>R</math>-module consisting of <math>m/s</math> with the operations defined above. As above, there is a canonical module homomorphism
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| ::φ: ''M'' → ''S''<sup>−1</sup>''M''
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| :mapping
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| ::φ(''m'') = ''m'' / 1.
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| The same notations for the localization of a ring are used for modules: <math>M_\mathfrak{p}</math> denote the localization of ''M'' at a prime ideal <math>\mathfrak{p}</math> and <math>M_f</math> the localization of a non-nilpotent element ''f''.
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| By the very definitions, the localization of the module is tightly linked to the one of the ring via the [[tensor product]]
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| :''S''<sup>−1</sup>''M'' = ''M'' ⊗<sub>''R''</sub>''S''<sup>−1</sup>''R'',
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| This way of thinking about localising is often referred to as [[extension of scalars]].
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| As a tensor product, the localization satisfies the usual [[universal property]].{{Clarify|date=March 2012}}
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| == Examples and applications ==
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| * Given a commutative ring ''R'', we can consider the [[multiplicative set]] ''S'' of non-zerodivisors (i.e. elements ''a'' of ''R'' such that multiplication by ''a'' is an injection from ''R'' into itself.) The ring ''S''<sup>−1</sup>''R'' is called the '''[[total quotient ring]]''' of ''R''. ''S'' is the largest multiplicative set such that the canonical mapping from ''R'' to ''S''<sup>−1</sup>''R'' is injective. When ''R'' is an integral domain, this is none other than the fraction field of ''R''.
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| * The ring [[modular arithmetic|'''Z'''/''n'''''Z''']] where ''n'' is [[composite number|composite]] is not an integral domain. When ''n'' is a [[prime number|prime]] power it is a finite [[local ring]], and its elements are either units or [[nilpotent]]. This implies it can be localized only to a zero ring. But when ''n'' can be factorised as ''ab'' with ''a'' and ''b'' [[coprime]] and greater than 1, then '''Z'''/''n'''''Z''' is by the [[Chinese remainder theorem]] isomorphic to '''Z'''/''a'''''Z''' × '''Z'''/''b'''''Z'''. If we take ''S'' to consist only of (1,0) and 1 = (1,1), then the corresponding localization is '''Z'''/''a'''''Z'''.
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| * Let ''R'' = '''Z''', and ''p'' a prime number. If ''S'' = '''Z''' - ''p'''''Z''', then ''R''* is the localization of the integers at ''p''.
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| * As a generalization of the previous example, let ''R'' be a commutative ring and let ''p'' be a prime ideal of ''R''. Then ''R'' - ''p'' is a multiplicative system and the corresponding localization is denoted ''R<sub>p</sub>''. The unique maximal ideal is then ''p''.
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| * Let ''R'' be a commutative ring and ''f'' an element of ''R''. we can consider the multiplicative system {''f<sup>n</sup>'' : ''n'' = 0,1,...}. Then the localization intuitively is just the ring obtained by inverting powers of ''f''. If ''f'' is nilpotent, the localization is the zero ring.
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| Two classes of localizations occur commonly in [[commutative algebra]] and [[algebraic geometry]] and are used to construct the rings of functions on [[open set|open subsets]] in [[Zariski topology]] of the [[spectrum of a ring]], Spec(''R'').
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| * The set ''S'' consists of all powers of a given element ''r''. The localization corresponds to restriction to the Zariski open subset ''U''<sub>''r''</sub> ⊂ Spec(''R'') where the function ''r'' is non-zero (the sets of this form are called ''principal Zariski open sets''). For example, if ''R'' = ''K''[''X''] is the [[polynomial ring]] and ''r'' = ''X'' then the localization produces the ring of [[Laurent polynomial]]s ''K''[''X'', ''X''<sup>−1</sup>]. In this case, localization corresponds to the embedding ''U'' ⊂ ''A''<sup>1</sup>, where ''A''<sup>1</sup> is the affine line and ''U'' is its Zariski open subset which is the complement of 0.
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| * The set ''S'' is the [[complement (set theory)|complement]] of a given [[prime ideal]] ''P'' in ''R''. The primality of ''P'' implies that ''S'' is a multiplicatively closed set. In this case, one also speaks of the "localization at ''P''". Localization corresponds to restriction to the complement ''U'' in Spec(''R'') of the [[irreducible component|irreducible]] Zariski closed subset ''V''(''P'') defined by the prime ideal ''P''.
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| == Properties ==
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| Some properties of the localization ''R*'' = ''S''<sup> −1</sup>''R'':
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| * The ring homomorphism ''R'' → ''S''<sup> −1</sup>''R'' is injective if and only if ''S'' does not contain any [[zero divisor]]s.
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| * There is a [[bijection]] between the set of prime ideals of ''S''<sup>−1</sup>''R'' and the set of prime ideals of ''R'' which do not intersect ''S''. This bijection is induced by the given homomorphism ''R'' → ''S''<sup> −1</sup>''R''.
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| * In particular: after localization at a prime ideal ''P'', one obtains a [[local ring]], or in other words, a ring with one maximal ideal, namely the ideal generated by the extension of P.
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| The localization of a module <math>M \to S^{-1}M</math> is a functor from the category of ''R''-modules to the category of <math>S^{-1}R</math>-modules. From the definition, one can see that it is [[exact functor|exact]], or in other words (reading this in the tensor product) that ''S''<sup>−1</sup>''R'' is a [[flat module]] over ''R''. This is actually foundational for the use of flatness in algebraic geometry, saying in particular that the inclusion of an [[open set]] in Spec(''R'') (see [[spectrum of a ring]]) is a [[flat morphism]].
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| The localization functor (usually) preserves Hom and tensor products in the following sense: the natural map
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| :<math>S^{-1}(M \otimes_R N) \to S^{-1}M \otimes_{S^{-1}R} S^{-1}N</math>
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| is an isomorphism and if <math>M</math> is finitely generated, the natural map
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| :<math>\operatorname{Hom}_R S^{-1}(M, N) \to \operatorname{Hom}_{S^{-1}R} (S^{-1}M, S^{-1}N)</math>
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| is an isomorphism.
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| If a module ''M'' is a [[finitely generated module|finitely generated]] over ''R'', we have: <math>S^{-1} M = 0</math> if and only if <math>t M = 0</math> for some <math>t \in S</math> if and only if <math>S</math> intersects the annihilator of ''M''.<ref>Borel, AG. 3.1</ref>
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| Let ''R'' be an integral domain with the field of fractions ''K''. Then its localization <math>R_\mathfrak{p}</math> at a prime ideal <math>\mathfrak{p}</math> can be viewed as a subring of ''K''. Moreover,
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| :<math>R = \cap_\mathfrak{p} R_\mathfrak{p} = \cap_\mathfrak{m} R_\mathfrak{m}</math>
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| where the first intersection is over all prime ideals and the second over the maximal ideals.<ref>Matsumura, Theorem 4.7</ref>
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| Let <math>\sqrt{I}</math> denote the radical of an ideal ''I'' in ''R''. Then
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| :<math>\sqrt{I} \cdot S^{-1}R = \sqrt{I \cdot S^{-1}R}</math>
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| In particular, ''R'' is [[reduced ring|reduced]] if and only if its total ring of fractions is reduced.<ref>Borel, AG. 3.3</ref>
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| == Stability under localization ==
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| Many properties of a ring are stable under localization. For example, the localization of a noetherian ring (resp. principal ideal domain) is noetherian (resp. principal ideal domain). The localization of an integrally closed domain is an integrally closed domain. In many cases, the converse also holds. (See below)
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| == Local property ==
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| Let ''M'' be a ''R''-module. We could think of two kinds of what it means some property ''P'' holds for ''M'' at a prime ideal <math>\mathfrak{p}</math>. One means that '' P'' holds for <math>M_\mathfrak{p}</math>; the other means that ''P'' holds for a neighborhood of <math>\mathfrak{p}</math>. The first interpretation is more common.<ref>Matsumura, a remark after Theorem 4.5</ref> But for many properties the first and second interpretations coincide. Explicitly, the second means the following conditions are equivalent.
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| *(i) ''P'' holds for ''M''.
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| *(ii) ''P'' holds for <math>M_\mathfrak{p}</math> for all prime ideal <math>\mathfrak{p}</math> of ''R''.
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| *(iii) ''P'' holds for <math>M_\mathfrak{m}</math> for all maximal ideal <math>\mathfrak{m}</math> of ''R''.
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| Then the following are local properties in the second sense.
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| * ''M'' is zero.
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| * ''M'' is torsion-free (when ''R'' is a domain)
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| * ''M'' is [[flat module|flat]].
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| * ''M'' is [[invertible|invertible module]] (when ''R'' is a domain and ''M'' is a submodule of the field of fractions of ''R'')
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| * <math>f: M \to N</math> is injective (resp. surjective) when ''N'' is another ''R''-module.
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| On the other hand, some properties are not local properties. For example, "noetherian" is (in general) not a local property: that is, to say there is a non-noetherian ring whose localization at every maximal ideal is noetherian: this example is due to Nagata.{{Citation needed|date=March 2012}}
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| == Support ==
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| The '''support of the module''' ''M'' is the set of prime ideals ''p'' such that ''M''<sub>''p''</sub> ≠ 0. Viewing ''M'' as a function from the [[spectrum of a ring|spectrum]] of ''R'' to ''R''-modules, mapping
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| :<math>p \mapsto M_p</math>
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| this corresponds to the [[support (mathematics)|support]] of a function.
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| ==(Quasi-)coherent sheaves==
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| In terms of localization of modules, one can define [[quasi-coherent sheaf|quasi-coherent sheaves]] and [[coherent sheaf|coherent sheaves]] on [[locally ringed space]]s. In algebraic geometry, the '''quasi-coherent''' ''O''<sub>''X''</sub>-'''modules''' for [[scheme (mathematics)|scheme]]s ''X'' are those that are locally modelled on sheaves on Spec(''R'') of localizations of any ''R''-module ''M''. A '''coherent''' ''O''<sub>''X''</sub>-'''module''' is such a sheaf, locally modelled on a [[finitely-presented module]] over ''R''.
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| == Non-commutative case ==
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| Localizing [[non-commutative ring]]s is more difficult; the localization does not exist for every set ''S'' of prospective units. One condition which ensures that the localization exists is the [[Ore condition]].
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| One case for non-commutative rings where localization has a clear interest is for rings of differential operators. It has the interpretation, for example, of adjoining a formal inverse ''D''<sup>−1</sup> for a differentiation operator D. This is done in many contexts in methods for [[differential equation]]s. There is now a large mathematical theory about it, named [[microlocal analysis|microlocalization]], connecting with numerous other branches. The ''micro-'' tag is to do with connections with [[Fourier theory]], in particular.
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| == See also ==
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| * [[Completion (ring theory)]]
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| * [[Valuation ring]]
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| * [[Overring]]
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| === Localization ===
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| [[:Category:Localization (mathematics)]]
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| * [[Local analysis]]
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| * [[Localization of a category]]
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| * [[Localization of a ring]]
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| * [[Localization of a module]]
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| * [[Localization of a topological space]]
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| * [[Local ring]]
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| == Notes ==
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| {{reflist}}
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| == References ==
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| *[[Armand Borel|Borel, Armand]]. Linear Algebraic Groups (2nd ed.). New York: Springer-Verlag. ISBN 0-387-97370-2.
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| * [[Serge Lang]], "Algebraic Number Theory," Springer, 2000. pages 3–4.
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| [[Category:Localization (mathematics)]]
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| [[Category:Module theory]]
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| [[Category:Commutative algebra]]
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| [[Category:Ring theory]]
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| [[de:Lokalisierung (Algebra)]]
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| [[fr:Localisation (mathématique)]]
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| [[ko:국소화 (환론)]]
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| [[zh:環的局部化]]
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The London schedule has long had cheerleaders for its talent on home territory, but in the past it has been squeezed out by more commercially robust cities.
Now it seems the capital is holding its ground against the bigger boys, as more and more international press, and buyers, make London an important stop in their schedule - blizzards in New York notwithstanding.
This in part has been due to brands like Burberry Prorsum, Mulberry and Tom Ford, which, with the weight of their advertising budgets behind them, command an international audience. Topshop, led by creative director Kate Phelan, also of British Vogue, has also helped provide financial support and a professional framework in which the creativity of London�s emerging designers can be showcased.
This situation has not gone unnoticed in Milan, where Giorgio Armani has taken Stella Jean under his wing, hosting her spring/summer 2014 show last September. �The new generation of Italian designers needs our support,� said Armani, echoing the sentiment that has long made London great
LVMH (the parent company of brands such as Louis Vuitton, Christian Dior and Celine Bags Outlet) is also taking lessons from London: on Thursday it announced a shortlist of 30 designers for its inaugural LVMH Young Fashion Designer Prize. With �300,000 (�246,000) at stake, plus a year of mentoring, the number of London designers shortlisted, including Simone Rocha, Thomas Tait, Meadham Kirchhoff and J JS Lee, is a clear indication of the capital�s fertile groun
Fittingly, the nominees - many of which have come through support programmes Newgen and Fashion East - are some of the most exciting shows on the schedul
Korean-born J JS Lee, who trained at Central Saint Martins, took the prized opening slot yesterday in rain-swept central London. For autumn/winter 2014 she showed an elegant collection of brushed mohair, plaid overcoats and formal dresses - experimenting with cocoon shapes, biker jackets and rounded shoulders for the former, while playing with different lengths for the latte
Cobalt blue houndstooth as a laser-cut detail and d�grad� printed silk provided a jolt of colour in a predominantly cream, navy and forest-green palette. Slim, long-line trousers were an elegant proposition for evenings, while chunky, cable knits were covetably co
.
The London College of Fashion MA Show at the Waldorf Astoria Hotel on day one of London Fashion Week yesterday (PA) With a fit-to-burst schedule of shows, presentations and parties over the next four days, there�s plenty to inspire and excite the fashion world - both on and off the catwa
JW Anderson�s first womenswear collection since LVMH bought a minority stake in his business last September is sure to be as controversial as ever: the designer�s gender-blurring take on dressing has its detractors, but just as many fans. The designer was also appointed creative director of Loewe, a Spanish leather brand within the stable, so an excellent accessories offering is to be expect
It was all change at Mulberry last season too, as Emma Hill departed after five years as creative director of the British brand. Hill seemed to have hit on a winning formula: balancing design and the right kind of celebrity endorsements fortified the brand�s finances, but recent profit warnings are cited as the reason for her departu
This season, the brand will not be hosting its usual catwalk extravaganza in Claridge�s ballroom. Instead it has announced a photocall at which Cara Delevingne, its campaign face, will reveal the brand�s next big move. Speculation is rife that she will be announced as creative director, but the brand�s success with bags named after It girls makes the debut of the �Cara� a far more likely prosp
Joseph, celebrating 25 years since its first west London boutique opened, is presenting on schedule for the first time too. It may not have the budgets of its blockbuster digital rivals, but it is held in esteem by serious shoppers and the fashion cr
While there is a respectable coterie of British luxury brands, it�s the commercial pull of the high street that is unrivalled, something the British Fashion Council - responsible for co-ordinating the schedule - has cottoned on to. As well as Topshop�s premium offering Unique, now a regular on the schedule, the BFC has courted brands such as River Island, which debuted its collaboration with Rihanna in London this time last y
r.
Now Whistles is presenting on the schedule for autumn/winter 2014; with a mens collection rumoured to be on the horizon and a flagship store on Mayfair�s Dover Street, the brand is certainly looking to exp
So too are Christopher Kane and Roksanda Ilincic, who plan to open boutiques on Mount Street this year.