On surjectivity in tensor triangular geometry
Category Theory
2024-09-27 v2 Algebraic Topology
Representation Theory
Abstract
We prove that a jointly conservative family of geometric functors between rigidly-compactly generated tensor triangulated categories induces a surjective map on Balmer spectra. From this we deduce a fiberwise criterion for Balmer's comparison map to be a continuous bijection. This gives short alternative proofs of the Hopkins--Neeman theorem and its generalization, due to Lau, to the case of a finite group acting trivially on an affine scheme.
Cite
@article{arxiv.2305.05604,
title = {On surjectivity in tensor triangular geometry},
author = {Tobias Barthel and Natalia Castellana and Drew Heard and Beren Sanders},
journal= {arXiv preprint arXiv:2305.05604},
year = {2024}
}
Comments
Accepted for publication in Math. Z.; comments still welcome!