Asymptotic vanishing of cohomology in triangulated categories

Fuente: arXiv
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Main Authors: Bergh, Petter Andreas, Jorgensen, David A., Thompson, Peder
Format: Preprint
Published: 2024
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_version_ 1866918314904649728
author Bergh, Petter Andreas
Jorgensen, David A.
Thompson, Peder
author_facet Bergh, Petter Andreas
Jorgensen, David A.
Thompson, Peder
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_12763
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Asymptotic vanishing of cohomology in triangulated categories
Bergh, Petter Andreas
Jorgensen, David A.
Thompson, Peder
K-Theory and Homology
Commutative Algebra
Category Theory
Rings and Algebras
16E30, 18G15, 18G80
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.
title Asymptotic vanishing of cohomology in triangulated categories
topic K-Theory and Homology
Commutative Algebra
Category Theory
Rings and Algebras
16E30, 18G15, 18G80
url https://arxiv.org/abs/2405.12763