Geometric Points in Tensor Triangular Geometry
Algebraic Topology
2026-03-27 v1 Commutative Algebra
Algebraic Geometry
Category Theory
Representation Theory
Abstract
In this paper, we study geometric points in tensor triangular geometry. In doing so, we construct a counter-example to Balmer's Nerves of Steel conjecture using free constructions in higher Zariski geometry. We then go on to introduce and discuss constructible spectra in the context of tensor triangular geometry. For tensor triangulated categories satisfying a mild enhancement condition, we use these spectra to construct geometric incarnations of (homological or triangular) primes via maps to "pointlike" tensor triangulated categories.
Keywords
Cite
@article{arxiv.2603.25664,
title = {Geometric Points in Tensor Triangular Geometry},
author = {Tobias Barthel and Logan Hyslop and Maxime Ramzi},
journal= {arXiv preprint arXiv:2603.25664},
year = {2026}
}
Comments
66 pages, comments welcome!