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Title: Weighted homological regularities

LetAAbe a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the homological and internal degrees of cochain complexes of gradedAA-modules, providing weighted versions of Castelnuovo–Mumford regularity, Tor-regularity, Artin–Schelter regularity, and concavity. In some cases an invariant (such as Tor-regularity) that is infinite can be replaced with a weighted invariant that is finite, and several homological invariants of complexes can be expressed as weighted homological regularities. We prove a few weighted homological identities some of which unify different classical homological identities and produce interesting new ones.

 
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Award ID(s):
2302087 2001015
NSF-PAR ID:
10506375
Author(s) / Creator(s):
; ;
Editor(s):
Dan Abramovich
Publisher / Repository:
Amer. Math. Soc.
Date Published:
Journal Name:
Transactions of the American Mathematical Society
ISSN:
0002-9947
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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