2012/08/31 by Petter Andreas Bergh, David A. Jorgensen, Steffen Oppermann
Mathematics · #Algebraic structures and combinatorial models #Cohomology #Commutative Algebra and Its Applications #Commutative property #Cup product #De Rham cohomology #Equivariant cohomology #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Local cohomology #Motivic cohomology #math.AC #math.CT #math.KT #math.RA #msc:13H10 #msc:16E40 #msc:16W50 #Čech cohomology
paper · pdf · doi:10.1112/blms/bdt094
14 pages
arxiv created 2012/09/06 · openalex publication_date 2014/01/09 · openalex created_date 2016/06/24 · arxiv updated 2017/05/17 · openalex updated_date 2026/08/05
We study Z-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 2. In particular, the products 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.