On the cohomology of simple Shimura varieties with non quasi-split local groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916593306435584 |
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| author | Chi, Jingren Haines, Thomas J. |
| author_facet | Chi, Jingren Haines, Thomas J. |
| contents | We study the Scholze test functions for bad reduction of simple Shimura varieties at a prime where the underlying local group is any inner form of a product of Weil restrictions of general linear groups. Using global methods, we prove that these test functions satisfy a vanishing property of their twisted orbital integrals, and we prove that the pseudostabilization base changes of such functions exist (even though the local group need not be quasi-split) and can be expressed in terms of explicit distributions in the stable Bernstein center. We then deduce applications to the stable trace formula and local Hasse-Weil zeta functions for these Shimura varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the cohomology of simple Shimura varieties with non quasi-split local groups Chi, Jingren Haines, Thomas J. Number Theory Algebraic Geometry Representation Theory We study the Scholze test functions for bad reduction of simple Shimura varieties at a prime where the underlying local group is any inner form of a product of Weil restrictions of general linear groups. Using global methods, we prove that these test functions satisfy a vanishing property of their twisted orbital integrals, and we prove that the pseudostabilization base changes of such functions exist (even though the local group need not be quasi-split) and can be expressed in terms of explicit distributions in the stable Bernstein center. We then deduce applications to the stable trace formula and local Hasse-Weil zeta functions for these Shimura varieties. |
| title | On the cohomology of simple Shimura varieties with non quasi-split local groups |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2501.12127 |