Class and rank of differential modules |
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Authors: | Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar |
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Affiliation: | (1) Department of Mathematics, University of Nebraska, Lincoln, 68588, NE, USA;(2) Department of Computer and Mathematical Sciences, University of Toronto at Scarborough, Toronto, ON, M1A 1C4, Canada |
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Abstract: | 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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