Vanishing theorems for Shimura varieties at unipotent level
| Autor: | Caraiani, A., Gulotta, D., Johansson, C. |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of the European Mathematical Society |
| Popis: | We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite $\Gamma_1(p^\infty)$-level (defined with respect to a Borel subgroup) vanishes above the middle degree, under the assumption that the group of the Shimura datum splits at $p$. This generalizes and strengthens the vanishing result proved in "Shimura varieties at level $\Gamma_1(p^\infty)$ and Galois representations". As an application of this vanishing theorem, we prove a result on the codimensions of ordinary completed homology for the same groups, analogous to conjectures of Calegari--Emerton for completed (Borel--Moore) homology. Comment: 38 pages, minor revisions to improve exposition |
| Databáze: | OpenAIRE |
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