构造具有指定上同调支撑的模
环与代数
2007-07-30 v2 交换代数
摘要
对于左 noether 环 R 上的有限生成模 M，相对于 R-模导出范畴上的中心上同调运算环 A，定义其上同调支撑 Supp_A(M)。证明若 A-模 Ext^R(M,M) 是 noether 的且对充分大的 i 有 Ext_i^R(M,R)=0，则 Supp_A(M) 的每个闭子集都是某个有限生成 R-模的支撑。该定理特化为群代数、局部完全交以及域上有限维代数上模的簇的已知可实现性结果。该定理还被用于构造交换局部 noether 环上大量有限投射维数的有限生成模。
引用
@article{arxiv.math/0702654,
title = {Constructing modules with prescribed cohomological support},
author = {Luchezar L. Avramov and Srikanth B. Iyengar},
journal= {arXiv preprint arXiv:math/0702654},
year = {2007}
}
备注
To appear in the Illinois Journal of Mathematics, the issue honoring Phillip Griffith. Revised version has 18 pages. A word (the first one) has been added to the title and the material has been reorganized into seven sections, in place of the original six. There are, however, no changes of any substance