Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted homological regularities   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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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: stat