Finite Schur filtration dimension for modules over an algebra with Schur filtration
Finite Schur filtration dimension for modules over an algebra with Schur filtration
复制标题
使用 Schur 过滤的代数上的模块的有限 Schur 过滤维数
DOI：
10.1007/s00031-009-9054-0
复制
发表时间：
2007
影响因子：
0.7
通讯作者：
W. Kallen
中科院分区：
文献类型：
--
作者：
V. Srinivas;W. Kallen
LetG= GLNor SLNas reductive linear algebraic group over a fieldkof characteristicp> 0. We prove several results that were previously established only whenN⩽ 5 orp> 2N: LetGact rationally on a finitely generated commutativek-algebraAand let grAbe the Grosshans graded ring. We show that the cohomology algebraH*(G, grA) is finitely generated overk. If moreoverAhas a good filtration andMis a NoetherianA-module with compatibleGaction, thenMhas finite good filtration dimension and theHi(G,M) are NoetherianAG-modules. To obtain results in this generality, we employ functorial resolution of the ideal of the diagonal in a product of Grassmannians.
