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| {{Refimprove|date=December 2009}}
| | Hello, my title is Andrew and my wife doesn't like it at all. My working day job is an invoicing officer but I've currently applied for an additional 1. Alaska is the only location I've been residing in but now I'm considering other options. To perform lacross is something I truly appreciate doing.<br><br>my blog - [http://isaworld.pe.kr/?document_srl=392088 tarot card readings] |
| In [[number theory]] and [[algebraic geometry]], the '''Tate twist''',<ref>'The Tate Twist', in Lecture Notes in Mathematics', Vol 1604, 1995, Springer, Berlin p.98-102</ref> named after [[John Tate]], is an operation on [[Galois module]]s.
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| For example, if ''K'' is a [[field (mathematics)|field]], ''G<sub>K</sub>'' is its [[absolute Galois group]], and ρ : ''G<sub>K</sub>'' → Aut<sub>'''Q'''<sub>''p''</sub></sub>(''V'') is a [[group representation|representation]] of ''G<sub>K</sub>'' on a finite-dimensional [[vector space]] ''V'' over the field '''Q'''<sub>''p''</sub> of [[p-adic number|''p''-adic numbers]], then the Tate twist of ''V'', denoted ''V''(1), is the representation on the [[tensor product of representations|tensor product]] ''V''⊗'''Q'''<sub>''p''</sub>(1), where '''Q'''<sub>''p''</sub>(1) is the [[cyclotomic character|''p''-adic cyclotomic character]] (i.e. the [[Tate module]] of the group of [[roots of unity]] in the separable closure ''K<sup>s</sup>'' of ''K''). More generally, if ''m'' is a [[positive integer]], the '''''m''th Tate twist of ''V''''', denoted ''V''(''m''), is the tensor product of ''V'' with the ''m''-fold tensor product of '''Q'''<sub>''p''</sub>(1). Denoting by '''Q'''<sub>''p''</sub>(−1) the [[dual representation]] of '''Q'''<sub>''p''</sub>(1), the ''-m''th Tate twist of ''V'' can be defined as
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| :<math>V\otimes\mathbf{Q}_p(-1)^{\otimes m}.</math>
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| ==References== | |
| <references/>
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| {{DEFAULTSORT:Tate Twist}}
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| [[Category:Number theory]]
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| [[Category:Algebraic geometry]]
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Latest revision as of 20:06, 15 November 2014
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