Support sets of pairs of modules
Support sets of pairs of modules
复制标题
支持成对模块组
DOI：
10.2140/pjm.2002.207.393
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发表时间：
2002
影响因子：
0.6
通讯作者：
David A. Jorgensen
中科院分区：
文献类型：
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作者：
David A. Jorgensen
设R是由f1，…，fc生成的真理想极小生成的局部整环(Q，n)的商。设Q/n是代数闭的，设M和N是有限生成的R-模。我们证明了在c维仿射空间中存在一个代数集，称为(M，N)对的支撑集，它描述了超曲面hE(f1，…，fc)-n(1，…，fc)上有无穷多个非零ExtIq/(H)(M，N)的超曲面.这将完全交上模的支撑簇的概念推广到正则局部环的任意商。
Let R be the quotient of a local domain (Q, n) by a proper ideal minimally generated by f 1 ,...,f c . Assume Q/ n is algebraically closed, and let M and N be finitely generated R-modules. We show there is an algebraic set in c-dimensional affine space, called the support set of the pair (M, N), which describes those hypersurfaces h E (f 1 ,...,f c )-n( 1 ,...,f c ) over which there are infinitely many nonzero Ext i Q/(h) (M,N). This generalizes to arbitrary quotients of regular local rings the notion of support variety for modules over complete intersections.