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arXiv · 2507.08566

Categorical K\"unneth formulas for analytic stacks

Youshua Kesting
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Abstract

In arXiv:0805.0157v5, the authors define a class of derived stacks, called "perfect stacks" and show that for this class the categories of quasi-coherent sheaves satisfy a categorical K\"unneth formula. Motivated to extend their results to the theory of analytic stacks as developed by Clausen-Scholze, we investigate categorical K\"unneth formulas for general $6$-functor formalisms. As applications we show a general Tannakian reconstruction result for analytic stacks and, following recent work of Ansch\"utz, Le Bras and Mann arXiv:2412.20968v1, show a $p$-adic version of Drinfeld's lemma for certain stacks that appear conjecturally in a categorical $p$-adic Langlands program.

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Youshua Kesting. 2025-07-11. Categorical K\"unneth formulas for analytic stacks. https://arxiv.org/abs/2507.08566

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