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 $G o H$ 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.
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机译：令$ k $为代数封闭字段。如果$ bG $是线性可归约的$ k $-group，而$ bH $是光滑代数$ k $-group，我们为组同态$ bG to bH $建立一个刚度属性直到$ bH（k）$通过共轭的自然作用。我们的主要结果表明，在任何基础变化$ K / k $和$ K $代数封闭的情况下，该集合保持不变。证明这是仿射组方案的Hochschild同源性消失的结果。
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