Perfectoid Shimura varieties and the Calegari-Emerton conjectures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911128263589888 |
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| author | Hansen, David Johansson, Christian |
| author_facet | Hansen, David Johansson, Christian |
| contents | We prove many new cases of a conjecture of Calegari-Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel-Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified Shimura varieties of pre-abelian type, generalizing previous work of Scholze. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_03951 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Perfectoid Shimura varieties and the Calegari-Emerton conjectures Hansen, David Johansson, Christian Number Theory Algebraic Geometry Representation Theory We prove many new cases of a conjecture of Calegari-Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel-Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified Shimura varieties of pre-abelian type, generalizing previous work of Scholze. |
| title | Perfectoid Shimura varieties and the Calegari-Emerton conjectures |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2011.03951 |