Categorical Künneth formulas for analytic stacks
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913938319343616 |
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| author | Kesting, Youshua |
| author_facet | Kesting, Youshua |
| contents | 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 Künneth formula. Motivated to extend their results to the theory of analytic stacks as developed by Clausen-Scholze, we investigate categorical Künneth formulas for general $6$-functor formalisms. As applications we show a general Tannakian reconstruction result for analytic stacks and, following recent work of Anschütz, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Categorical Künneth formulas for analytic stacks Kesting, Youshua Algebraic Geometry Number Theory 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 Künneth formula. Motivated to extend their results to the theory of analytic stacks as developed by Clausen-Scholze, we investigate categorical Künneth formulas for general $6$-functor formalisms. As applications we show a general Tannakian reconstruction result for analytic stacks and, following recent work of Anschütz, 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. |
| title | Categorical Künneth formulas for analytic stacks |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2507.08566 |