IUTを読むための用語集資料スレ2

**１３２人目の素数さん** · 2020/12/01(火) 18:11:43.01

テンプレは後で

**１３２人目の素数さん** · 2021/07/05(月) 06:28:26.45

>>114
>Tate 捻り

下記Tate twist みたいだね
但し、下記は”an operation on Galois modules”とあるので
星先生の記述とはちょっと違うような
つまり、星先生の記述は、”an operation ”ではなく、それが集まった、例えば群のような集合を意味している気がする

（参考：文字化けは面倒なので修正しませんので、原文ご参照）
https://en.wikipedia.org/wiki/Tate_twist
Tate twist
In number theory and algebraic geometry, the Tate twist,[1] 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
{\displaystyle V\otimes \mathbf {Q} _{p}(-1)^{\otimes m}.}{\displaystyle V\otimes \mathbf {Q} _{p}(-1)^{\otimes m}.}
References
[1] 'The Tate Twist', in Lecture Notes in Mathematics', Vol 1604, 1995, Springer, Berlin p.98-102

**１３２人目の素数さん** · 2021/07/05(月) 06:48:13.60

>>115
>Tate twist

下記が参考になりそう
日本語では、圧倒的に情報量が少ない
それと”What is the intuition behind the concept of Tate twists?”と質問する姿勢は見習うべきでしょうね

https://math.stackexchange.com/questions/2923709/about-the-definition-of-l-adic-tate-twist
About the definition of l-adic Tate-twist asked Sep 20 '18 at 6:30 Elvis Torres Perez
(抜粋)
Zl(0)=Zl , Zl(1)=lim←?(μli), Zl(n+1)=Zl(n)?ZlZl(1) for n＞＝0

https://math.stackexchange.com/questions/57750/what-is-the-intuition-behind-the-concept-of-tate-twists/57757
What is the intuition behind the concept of Tate twists? asked Aug 16 '11 at 4:06 Nicole