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arXiv · 2603.26492

The motivic tt-geometry of real quadrics

Jean Paul Schemeil
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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.

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Jean Paul Schemeil. 2026-03-27. The motivic tt-geometry of real quadrics. https://arxiv.org/abs/2603.26492

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