Stratification and the comparison between homological and tensor triangular support
Algebraic Topology
2023-01-05 v2 Algebraic Geometry
Category Theory
Representation Theory
Abstract
We compare the homological support and tensor triangular support for `big' objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the homological spectrum to the tensor triangular spectrum is a bijection and that the two notions of support coincide whenever the category is stratified, extending work of Balmer. Moreover, we clarify the relations between salient properties of support functions and exhibit counter-examples highlighting the differences between homological and tensor triangular support.
Cite
@article{arxiv.2106.16011,
title = {Stratification and the comparison between homological and tensor triangular support},
author = {Tobias Barthel and Drew Heard and Beren Sanders},
journal= {arXiv preprint arXiv:2106.16011},
year = {2023}
}
Comments
18 pages, comments welcome. v2 - updated to include referee comments. Version to appear in The Quarterly Journal of Mathematics