Geodesic
Vanishing of Hochschild cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups.
Documenta mathematica, Tome 14 (2009), pp. 653-672.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $k$ be an algebraically closed field. If $\bG$ is a linearly reductive $k$--group and $\bH$ is a smooth algebraic $k$--group, we establish a rigidity property for the set of group homomorphisms $\bG \to \bH$ up to the natural action of $\bH(k)$ by conjugation. Our main result states that this set remains constant under any base change $K/k$ with $K$ algebraically closed. This is proven as consequence of a vanishing result for Hochschild cohomology of affine group schemes.
Classification : 20G05
Keywords: group schemes, representations, linearly reductive group, deformation theory 
@article{DOCMA_2009__14__a6,
     author = {Margaux, Benedictus},
     title = {Vanishing of {Hochschild} cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups.},
     journal = {Documenta mathematica},
     pages = {653--672},
     publisher = {mathdoc},
     volume = {14},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a6/}
}
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Margaux, Benedictus. Vanishing of Hochschild cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups.. Documenta mathematica, Tome 14 (2009), pp. 653-672. http://geodesic.mathdoc.fr/item/DOCMA_2009__14__a6/