A MODERN PROOF OF CHEVALLEY’S THEOREM ON ALGEBRAIC GROUPS

Abstract

Let k be a field, and let G be an algebraic group over k, by which we mean a connected smooth k-group scheme (not necessarily affine). Recall that such a G is automatically separated, finite type, and geometrically integral over k [4, Exp VIA, 0.3, 2.1.2, 2.4]. The most important classes of algebraic groups are the affine algebraic groups (also called linear algebraic groups, since affine algebraic groups coincide with the closed