Point Counting on Igusa Varieties for function fields
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866917057140883456 |
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| author | Hamacher, Paul Kim, Wansu |
| author_facet | Hamacher, Paul Kim, Wansu |
| contents | Igusa varieties over the special fibre of Shimura varieties have demonstrated many applications to the Langlands program via Mantovan's formula and Shin's point counting method. In this paper we study Igusa varieties over the moduli stack of global $\Gscr$-shtukas and (under certain conditions) calculate the Hecke action on its cohomology. As part of their construction we prove novel results about local $G$-shtukas in both equal and unequal characteristic and also discuss application of these results to Barsotti-Tate groups and Shimura varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01069 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Point Counting on Igusa Varieties for function fields Hamacher, Paul Kim, Wansu Algebraic Geometry Number Theory 14G35, 14H60 Igusa varieties over the special fibre of Shimura varieties have demonstrated many applications to the Langlands program via Mantovan's formula and Shin's point counting method. In this paper we study Igusa varieties over the moduli stack of global $\Gscr$-shtukas and (under certain conditions) calculate the Hecke action on its cohomology. As part of their construction we prove novel results about local $G$-shtukas in both equal and unequal characteristic and also discuss application of these results to Barsotti-Tate groups and Shimura varieties. |
| title | Point Counting on Igusa Varieties for function fields |
| topic | Algebraic Geometry Number Theory 14G35, 14H60 |
| url | https://arxiv.org/abs/2208.01069 |