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Tate twist — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Tate_twist
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T19:45:32.871Z
SHA-256 of the archived text: a794ab086929d5b007e1c80fae0d3fcc941abf068ca65124bb0bf64a729d35e8
Stable URL of this page: https://metraipolis.com/documento/dc_ddffebb8ef41

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Tate twist — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Tate_twist (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_ddffebb8ef41 (Metraipolis archive dc_ddffebb8ef41, sha256 a794ab086929d5b007e1c80fae0d3fcc941abf068ca65124bb0bf64a729d35e8)

BibTeX

@misc{dcddffebb8ef41,
  title = {Tate twist — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Tate_twist},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_ddffebb8ef41; sha256 a794ab086929d5b007e1c80fae0d3fcc941abf068ca65124bb0bf64a729d35e8},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Tate_twist. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In number theory and algebraic geometry, the Tate twist, named after John Tate, is an operation on Galois modules. For example, if K is a field, GK is its absolute Galois group, and ρ : GK → AutQp(V) is a representation of GK on a finite-dimensional vector space V over the field Qp of p-adic numbers, then the Tate twist of V, denoted V(1), is the representation on the tensor product V⊗Qp(1), where Qp(1) is the p-adic cyclotomic character (i.e. the Tate module of the group of roots of unity in the separable closure Ks of K). More generally, if m is a positive integer, the mth Tate twist of V, denoted V(m), is the tensor product of V with the m-fold tensor product of Qp(1). Denoting by Qp(−1) the dual representation of Qp(1), the −mth Tate twist of V can be defined as V ⊗ Q p ( − 1 ) ⊗ m . {\displaystyle V\otimes \mathbf {Q} _{p}(-1)^{\otimes m}.}

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Number theory»).
Fonte: Wikipedia in inglese, voce «Tate twist» — https://en.wikipedia.org/wiki/Tate_twist
Wikidata Q7687984 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q7687984
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Tate_twist?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1320164327, consultata il 2026-10-07T19:07:00.184Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: b7f5f2ce4cf7a92cc2f06f1adcf476bb21692bf1a97615d870286109d1fdaa8b