Lang's theorem
id:
lang-s-theorem-200-12101658
title:
Lang's theorem
text:
In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field F q , then, writing σ : G → G , x ↦ x q for the Frobenius, the morphism of varieties is surjective. Note that the kernel of this map is precisely G . The theorem implies that H 1 = H e ´ t 1
vanishes, and, consequently, any G-bundle on Spec F q is isomorphic to the trivial one. Also, the theorem plays a basic role in the theory of finite groups of Lie type.
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Lang%27s_theorem
date created:
date modified:
2022-02-15T14:38:32Z
main entity:
{"identifier":"Q6487014","url":"https://www.wikidata.org/entity/Q6487014"}
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fields total:
13
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