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arXiv · 2602.20835

The formal spectrum of a tensor-triangulated category

Drew Heard·Marius Nielsen
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Abstract

To any essentially small tensor-triangulated category $\mathcal{K}$ and Thomason subset $Y \subseteq \mathrm{Spc}(\mathcal{K})$ we associate a ringed space $(\mathrm{Spf}(\mathcal{K},Y), \mathcal{O}_{\mathrm{Spf}(\mathcal{K},Y)}),$ called the formal spectrum of $(\mathcal{K},Y)$. We establish basic properties of this construction and compute it in several examples from algebraic geometry, chromatic homotopy theory, equivariant homotopy theory, and modular representation theory.

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Drew Heard, Marius Nielsen. 2026-02-24. The formal spectrum of a tensor-triangulated category. https://arxiv.org/abs/2602.20835

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