Lang's theorem: Difference between revisions

Revision as of 19:06, 11 March 2014

Revision as of 19:07, 11 March 2014

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vanishes, and, consequently, any [[torsor (algebraic geometry)|''G''-bundle]] on <math>\operatorname{Spec} \mathbf{F}_q</math> is isomorphic to the trivial one. Also, the theorem plays a basic role in the theory of [[finite groups of Lie type]].

It is not necessary that ''G'' is affine. Thus, the theorem also applies to [[abelian variety|abelian varieties]] (e.g., [[elliptic curve]]s.) . In fact, this application was Lang's initial motivation.

== Proof ==