%AKirkman, E.%AWon, R.%AZhang, J.%ADan Abramovich Ed.%BJournal Name: Transactions of the American Mathematical Society
%D2023%IAmer. Math. Soc.
%JJournal Name: Transactions of the American Mathematical Society
%K
%MOSTI ID: 10506375
%PMedium: X
%TWeighted homological regularities
%XLet$A$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 Castelnuovoâ€“Mumford regularity, Tor-regularity, Artinâ€“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.

%0Journal Article