Asymptotic vanishing of cohomology in triangulated categories
Petter Andreas Bergh, David A. Jorgensen, Peder Thompson

TL;DR
This paper investigates the behavior of cohomology in triangulated categories, demonstrating that finite generation over a central ring leads to predictable asymptotic vanishing patterns, with broad applications.
Contribution
It establishes a link between finite generation of cohomology and asymptotic vanishing in triangulated categories, providing new insights and applications.
Findings
Finite generation over a central ring implies well-behaved asymptotic vanishing.
Enough consecutive vanishing leads to eventual vanishing of cohomology.
Several key applications demonstrate the theory's utility.
Abstract
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 generated over the ring acting centrally, then the asymptotic vanishing of the cohomology is well-behaved. In particular, enough consecutive asymptotic vanishing of cohomology implies all eventual vanishing. Several key applications are also given.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Operator Algebra Research
