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

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Let k be an algebraically closed field. If G is a linearly reductive k-group and H is a smooth algebraic k-group, we establish a rigidity property for the set of group homomorphisms G→H up to the natural action of H(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.
DOI : 10.4171/dm/284
Classification : 20G05
Mots-clés : representations, deformation theory, group schemes, linearly reductive group 
Benedictus Margaux. Vanishing of Hochschild cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups. Documenta mathematica, Tome 14 (2009), pp. 653-672. doi: 10.4171/dm/284
@article{10_4171_dm_284,
     author = {Benedictus Margaux},
     title = {Vanishing of {Hochschild} cohomology for affine group schemes and rigidity of homomorphisms between algebraic groups},
     journal = {Documenta mathematica},
     pages = {653--672},
     year = {2009},
     volume = {14},
     doi = {10.4171/dm/284},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/284/}
}
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