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The additivity of traces in stable $\infty$-categories

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arxiv 2109.01512 v3 pith:TO2XPCZD submitted 2021-09-03 math.KT math.ATmath.CT

Maxime Ramzi This is my paper · ORCID
classification math.KTmath.ATmath.CT
keywords inftymathbfadditivitycategoriesstabletracesmathrmmonoidal
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abstract

We prove a version of J.P. May's theorem on the additivity of traces, in symmetric monoidal stable $\infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an invariant of stable $\infty$-categories and construct a morphism of spectra $\mathrm{THH}(\mathbf C)\to \mathrm{End}(\mathbf 1_\mathbf C)$ for $\mathbf C$ a stably symmetric monoidal rigid $\infty$-category. We also explain how to get a more general statement involving traces of finite (homotopy) colimits.

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Cited by 1 Pith paper

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  1. Additivity of non-acyclicity classes for constructible \'etale sheaves

    math.AG 2025-05 conditional novelty 6.0 of 10

    The non-acyclicity class of a constructible etale sheaf is additive across distinguished triangles, under a cohomological smoothness assumption.

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