A short proof is given for Chevalley's theorem on algebraic groups as extensions of Abelian varieties by linear groups, while addressing Bertini's irreducibility theorem.
[ E xtraits du S \'eminaire B ourbaki, 1957--1962.] , Secr\'etariat math\'ematique, Paris, 1962
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Theorems of Bertini and Chevalley
A short proof is given for Chevalley's theorem on algebraic groups as extensions of Abelian varieties by linear groups, while addressing Bertini's irreducibility theorem.