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 
@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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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

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