48 citations · 140 across the 46 of their papers we have counts for
12 papers · 1 filter
Multiplicity in triangulated categories
Petter Andreas Bergh, David A. Jorgensen, Peder Thompson
We lay out the theory of a multiplicity in the setting of a triangulated category having a central ring action from a graded-commutative ring , in other words, an -linear tri…
Asymptotic vanishing of cohomology in triangulated categories
Petter Andreas Bergh, David A. Jorgensen, Peder Thompson
Given a graded-commutative ring acting centrally on a triangulated category, our main result shows that if cohomology of a pair of objects of the triangulated category is finitely…
Homology of complexes over finite tensor categories
Petter Andreas Bergh
We generalize a recent result by J.F. Carlson to finite tensor categories having finitely generated cohomology. Specifically, we show that if the Krull dimension of the cohomology…
Categorical matrix factorizations
Petter Andreas Bergh, David A. Jorgensen
In this paper we give a purely categorical construction of d-fold matrix factorizations of a natural transformation, for any even integer d. This recovers the classical definition…
Matrix factorizations for quantum complete intersections
Petter Andreas Bergh, Karin Erdmann
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposa…
Tate-Hochschild homology and cohomology of Frobenius algebras
Petter Andreas Bergh, David A. Jorgensen
We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negat…