Asymptotic vanishing of cohomology in triangulated categories
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |