Class and rank of differential modules

被引:29
作者
Avramov, Luchezar L. [1 ]
Buchweitz, Ragnar-Olaf
Iyengar, Srikanth
机构
[1] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA
[2] Univ Toronto Scarborough, Dept Comp & Math Sci, Toronto, ON M1A 1C4, Canada
基金
美国国家科学基金会;
关键词
D O I
10.1007/s00222-007-0041-6
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class - a substitute for the length of a free complex - and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.
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页码:1 / 35
页数:35
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