Very Schwartz coidempotents and continuous spectrum

Ko Aoki

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arXiv · 2505.04817

Very Schwartz coidempotents and continuous spectrum

Ko Aoki

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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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BibTeX RIS

Ko Aoki. 2025-05-07. Very Schwartz coidempotents and continuous spectrum. https://arxiv.org/abs/2505.04817

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