Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The negative side of cohomology for Calabi-Yau categories   We study integer-graded cohomology rings defined over Calabi-Yau categories.
We show that the cohomology in negative degree is a trivial extension of the
cohomology ring in non-negative degree, provided the latter admits a regular
sequence of central elements of length two. In particular, the product of
elements of negative degrees are zero. As corollaries we apply this to
Tate-Hochschild cohomology rings of symmetric algebras, and to Tate cohomology
rings over group algebras. We also prove similar results for Tate cohomology
rings over commutative local Gorenstein rings.

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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int