Wang Jianpan.INVERSE LIMITS OF AFFINE GROUP SCHEMES[J].Chinese Annals of Mathematics B,1988,9(4):418~428
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Authors：
Wang Jianpan;
Abstract：
This paper considers inverse systems of affine group schemes. The author establishes the existence of the limit of such a system and proves some properties of the limit some about its structure and some about its representations and cohomologies. In particular, a new explanation of generic cohomology is obtained: Let $\[\tilde G\]$ be the inverse limit of the following inverse system
$$\[G \leftarrow G \leftarrow G \leftarrow \cdots \]$$
where F is a Frobenius morphism of a linear algebraic group G. Then the generic cohomology of G(with respect to F）with coefficients in a rational G-module V is simply the
rational cohomology of $\[\tilde G\]$ with coefficients in V.
