Let be an algebraically closed field. If is a linearly reductive -group and is a smooth algebraic -group, we establish a rigidity property for the set of group homomorphisms up to the natural action of by conjugation. Our main result states that this set remains constant under any base change with algebraically closed. This is proven as consequence of a vanishing result for Hochschild cohomology of affine group schemes.
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Benedictus Margaux, Vanishing of Hochschild cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups. Doc. Math. 14 (2009), pp. 653–672DOI 10.4171/DM/284