Perverse sheaves on twisted affine flag varieties and Langlands duality
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916468319322112 |
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| author | Çiloğlu, Rızacan |
| author_facet | Çiloğlu, Rızacan |
| contents | We provide a description of Iwahori-Whittaker equivariant perverse sheaves on affine flag varieties associated to tamely ramified reductive groups, in terms of Langlands dual data. This extends the work of Arkhipov-Bezrukavnikov from the case of split reductive groups. To achieve this, we first extend the theory of Wakimoto sheaves to our context and prove convolution exact central objects admit a filtration by such. We then establish the tilting property of the Iwahori-Whittaker averaging of certain central objects arising from the geometric Satake equivalence, which enables us to address the absence of an appropriate analogue of Gaitsgory's central functor for non-split groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Perverse sheaves on twisted affine flag varieties and Langlands duality Çiloğlu, Rızacan Representation Theory Algebraic Geometry We provide a description of Iwahori-Whittaker equivariant perverse sheaves on affine flag varieties associated to tamely ramified reductive groups, in terms of Langlands dual data. This extends the work of Arkhipov-Bezrukavnikov from the case of split reductive groups. To achieve this, we first extend the theory of Wakimoto sheaves to our context and prove convolution exact central objects admit a filtration by such. We then establish the tilting property of the Iwahori-Whittaker averaging of certain central objects arising from the geometric Satake equivalence, which enables us to address the absence of an appropriate analogue of Gaitsgory's central functor for non-split groups. |
| title | Perverse sheaves on twisted affine flag varieties and Langlands duality |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2411.02648 |