The motivic tt-geometry of real quadrics
Algebraic Geometry
2026-03-30 v1 Algebraic Topology
Category Theory
K-Theory and Homology
Abstract
We study the tensor-triangular geometry of the category of Voevodsky motives generated by real quadrics. At the prime 2, we determine its Balmer spectrum, and find that it is a countably infinite, non-Noetherian space of Krull dimension 2. We detail the relationship between this space, the real Artin-Tate spectrum computed by Balmer-Gallauer, and Vishik's isotropic points. We conclude by combining our computation with Balmer-Gallauer's results on Artin-Tate motives to obtain a full description of the spectrum of integral motives of quadrics over real algebraic numbers.
Keywords
Cite
@article{arxiv.2603.26492,
title = {The motivic tt-geometry of real quadrics},
author = {Jean Paul Schemeil},
journal= {arXiv preprint arXiv:2603.26492},
year = {2026}
}