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Very Schwartz coidempotents and continuous spectrum

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arxiv 2505.04817 v1 pith:6I5YDUNK submitted 2025-05-07 math.CT math.AGmath.ATmath.GN

Ko Aoki This is my paper · ORCID
classification math.CTmath.AGmath.ATmath.GN
keywords compactcasecontinuousidempotentsschwartzspacesspectrumstable
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abstract

We introduce the continuous version of the (unstable) smashing spectrum functor. In the stable case, it assigns to each dualizably symmetric monoidal stable presentable $\infty$-category a stably compact space whose open subsets correspond to very Schwartz idempotents -- a certain class of idempotents we define. As an application, we prove Tannaka duality for spectral sheaves on stably compact spaces, including the case of compact Hausdorff spaces.

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  1. Dualizable Additive Categories

    math.AT 2026-08 conditional novelty 8.0 of 10

    Dualizable additive categories are characterized intrinsically and via almost modules, and a universal finitary localizing invariant (prestable motives) is constructed whose unit corepresents algebraic K-theory.

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