Affine weakly regular tensor triangulated categories
Category Theory
2016-10-05 v2 Algebraic Topology
K-Theory and Homology
Abstract
We prove that the Balmer spectrum of a tensor triangulated category is homeomorphic to the Zariski spectrum of its graded central ring, provided the triangulated category is generated by its tensor unit and the graded central ring is noetherian and regular in a weak sense. There follows a classification of all thick subcategories, and the result extends to the compactly generated setting to yield a classification of all localizing subcategories as well as the analog of the telescope conjecture. This generalizes results of Shamir for commutative ring spectra.
Cite
@article{arxiv.1511.02395,
title = {Affine weakly regular tensor triangulated categories},
author = {Ivo Dell'Ambrogio and Donald Stanley},
journal= {arXiv preprint arXiv:1511.02395},
year = {2016}
}
Comments
14 pages, several slight improvements. Final version, to appear in Pacific J Math