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arXiv · 2107.07474

Homological regularities and concavities

Ellen Kirkman·Robert Won·James J. Zhang
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Abstract

This paper concerns homological notions of regularity for noncommutative algebras. Properties of an algebra $A$ are reflected in the regularities of certain (complexes of) $A$-modules. We study the classical Tor-regularity and Castelnuovo-Mumford regularity, which were generalized from the commutative setting to the noncommutative setting by J{\o}rgensen and Dong-Wu. We also introduce two new numerical homological invariants: concavity and Artin-Schelter regularity. Artin-Schelter regular algebras occupy a central position in noncommutative algebra and noncommutative algebraic geometry, and we use these invariants to establish criteria which can be used to determine whether a noetherian connected graded algebra is Artin-Schelter regular.

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Ellen Kirkman, Robert Won, James J. Zhang. 2021-07-15. Homological regularities and concavities. https://arxiv.org/abs/2107.07474

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