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arXiv · 1208.5785

The negative side of cohomology for Calabi-Yau categories

Petter Andreas Bergh·David A. Jorgensen·Steffen Oppermann
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Abstract

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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Petter Andreas Bergh, David A. Jorgensen, Steffen Oppermann. 2012-09-06. The negative side of cohomology for Calabi-Yau categories. https://doi.org/10.1112/blms%2Fbdt094

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