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摘要翻译：
设G是GL_N或SL_N为正特征P域k上的约化线性代数群。我们证明了以前只有当N<6或p>2^N时才成立的几个结果。设G有理地作用于有限生成交换K-代数a。假定a作为G-模具有良好的过滤或Schur过滤。设M是具有相容G作用的noetherian a-模。那么M具有有限的Good/Schur过滤维数，使得最多有有限个非零的H^i(G，M)。而且这些H^I(G，M)是不变量环A^G上的noetherian模。我们的主要工具是一个包含Grassmannian乘积中对角理想的Schur函子的分解。
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英文标题：
《Finite Schur filtration dimension for modules over an algebra with Schur
filtration》
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作者：
Vasudevan Srinivas and Wilberd van der Kallen
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.
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PDF链接：
https://arxiv.org/pdf/0706.0604
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