Separable extensions in tensor-triangular geometry and generalized Quillen stratification
Category Theory
2024-09-10 v4 Algebraic Geometry
Algebraic Topology
Representation Theory
Abstract
We study the continuous map induced on spectra by a separable extension of tensor-triangulated categories. We determine the image of this map and relate the cardinality of its fibers to the degree of the extension. We then prove a weak form of descent, "up-to-nilpotence", which allows us to generalize Quillen's Stratification Theorem to equivariant derived categories.
Cite
@article{arxiv.1309.1808,
title = {Separable extensions in tensor-triangular geometry and generalized Quillen stratification},
author = {Paul Balmer},
journal= {arXiv preprint arXiv:1309.1808},
year = {2024}
}
Comments
Final revised version, 17 pages, to appear in Ann. Sci. Ecole Norm. Sup. (4). Formula in Thm.3.4(c) corrected