Bifunctor cohomology and cohomological finite generation for reductive groups
Bifunctor cohomology and cohomological finite generation for reductive groups
复制标题
还原群的双函子上同调和上同调有限生成
DOI：
10.1215/00127094-2009-065
复制
发表时间：
2008
影响因子：
2.5
通讯作者：
W. Kallen
中科院分区：
文献类型：
--
作者：
Antoine Touz'e;W. Kallen
设G是域k上的约化线性代数群，A是有限生成的交换k-代数，G通过k-代数自同构有理作用。不变量理论认为不变量环AG=H0(G，A)是有限生成的。证明了完全上同调环H-∗(G，A)实际上是有限生成的。证明是基于[22]中构造的严格多项式双函子上同调类。我们还继续研究Γ∗(gl(1))的双函子上同调。
Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory states that the ring of invariants AG=H0(G,A) is finitely generated. We show that in fact the full cohomology ring H∗(G,A) is finitely generated. The proof is based on the strict polynomial bifunctor cohomology classes constructed in [22]. We also continue the study of bifunctor cohomology of Γ∗(gl(1))