Regularity bounds for complexes and their homology

Autor(en): Nguyen, Hop D.
Stichwörter: ASYMPTOTIC-BEHAVIOR; DEPTH; HOMOMORPHISMS; IDEAL; Mathematics; MATRIX; RESOLUTION
Erscheinungsdatum: 2015
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Volumen: 159
Ausgabe: 2
Startseite: 355
Seitenende: 377
Zusammenfassung: 
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 Romer. For a bounded complex of finitely generated graded R-modules L, we prove the equality reg L = max(i is an element of Z){reg H-i(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.
ISSN: 03050041
DOI: 10.1017/S0305004115000390

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