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Regularity bounds for complexes and their homology

Published online by Cambridge University Press:  02 July 2015

HOP D. NGUYEN
HOP D. NGUYEN*
Affiliation:
Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genoa, Italy. Fachbereich Mathematik/Informatik, Institut für Mathematik, Universität Osnabrück, Albrectstr. 28a, 49069 Osnabrück, Germany. e-mail: [email protected]
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Abstract

Let R be a standard graded algebra over a field k. We prove an Auslander–Buchsbaum formula for the absolute Castelnuovo–Mumford regularity, extending important cases of previous works of Chardin and Römer. For a bounded complex of finitely generated graded R-modules L, we prove the equality reg L = maxi ∈$_{\mathbb Z}$ {reg Hi(L) − i} given the condition depth Hi(L) ⩾ dim Hi+1(L) - 1 for all i < sup L. As applications, we recover previous bounds on regularity of Tor due to Caviglia, Eisenbud–Huneke–Ulrich, among others. We also obtain strengthened results on regularity bounds for Ext and for the quotient by a linear form of a module.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 2 , September 2015 , pp. 355 - 377
Copyright
Copyright © Cambridge Philosophical Society 2015 

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