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arXiv · 2204.06679

Weighted homological regularities

Ellen Kirkman·Robert Won·James J. Zhang
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Abstract

Let $A$ be 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 graded $A$-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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Ellen Kirkman, Robert Won, James J. Zhang. 2022-04-14. Weighted homological regularities. https://arxiv.org/abs/2204.06679

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