Class and rank of differential modules

• Autores: Luchezar L. Avramov, Ragnar-Olaf Buchweitz, Srikanth B. Iyengar
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 169, Nº. 1, 2007, págs. 1-35
• Idioma: inglés
• DOI: 10.1007/s00222-007-0041-6
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• Resumen

  • 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.