## 2012年5月15日火曜日

### 素数に結び付いた結び目とは何か？（第六話）

English version

What is the knot associated to a prime?

#### 1 件のコメント:

1. Artin-Verdier duality came from Tate duality and generalizes it.

on en.wiki

In mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by Artin and Verdier (1964), that generalizes Tate duality.

In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic number field or local field, introduced by Tate (1962) and Poitou (1967).

Local Tate duality says there is a perfect pairing of finite groups

H^r(k,M)\times H^{2-r}(k,M')\rightarrow H^2(k,G_m)=Q/Z

where M is a finite group scheme and M′ its dual Hom(M,G_m).