Derived geometric Satake equivalence on the Beilinson-Drinfeld Grassmannian with one leg in mixed characteristic
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918386351472640 |
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| author | Bando, Katsuyuki |
| author_facet | Bando, Katsuyuki |
| contents | Fargues-Scholze developed a framework for the geometric Langlands program on the Fargues-Fontaine curve. In particular, they proved the geometric Satake equivalence on the moduli space of closed Cartier divisors on the curve. We prove the derived version of this equivalence with one leg. Namely, we show that the derived category of etale sheaves on the local Hecke stack is equivalent to the category of L-group-equivariant perfect complexes over the symmetric algebra of the shifted and (-1)-Tate-twisted Lie algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derived geometric Satake equivalence on the Beilinson-Drinfeld Grassmannian with one leg in mixed characteristic Bando, Katsuyuki Number Theory Algebraic Geometry Representation Theory 14D24, 14G45, 14M15 Fargues-Scholze developed a framework for the geometric Langlands program on the Fargues-Fontaine curve. In particular, they proved the geometric Satake equivalence on the moduli space of closed Cartier divisors on the curve. We prove the derived version of this equivalence with one leg. Namely, we show that the derived category of etale sheaves on the local Hecke stack is equivalent to the category of L-group-equivariant perfect complexes over the symmetric algebra of the shifted and (-1)-Tate-twisted Lie algebra. |
| title | Derived geometric Satake equivalence on the Beilinson-Drinfeld Grassmannian with one leg in mixed characteristic |
| topic | Number Theory Algebraic Geometry Representation Theory 14D24, 14G45, 14M15 |
| url | https://arxiv.org/abs/2603.12542 |