Matches in DBpedia 2014 for { ?s ?p In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field , then, writing for the Frobenius, the morphism of varieties is surjective. Note that the kernel of this map (i.e., ) is precisely .The theorem implies that vanishes, and, consequently, any G-bundle on 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.. }
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- Lang's_theorem comment "In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field , then, writing for the Frobenius, the morphism of varieties is surjective. Note that the kernel of this map (i.e., ) is precisely .The theorem implies that vanishes, and, consequently, any G-bundle on 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.".