Vanishing theorems for Shimura varieties at unipotent level
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| Title: | Vanishing theorems for Shimura varieties at unipotent level |
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| Authors: | Caraiani, Ana, Gulotta, Daniel R., Johansson, Christian, 1985 |
| Source: | Journal of the European Mathematical Society. 25(3):869-911 |
| Subject Terms: | p-adic automorphic forms, perfectoid spaces, Locally symmetric spaces |
| Description: | We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite Γ1.p1/-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 [A. Caraiani et al., Compos. Math. 156 (2020)]. 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. |
| File Description: | electronic |
| Access URL: | https://research.chalmers.se/publication/535687 https://research.chalmers.se/publication/535687/file/535687_Fulltext.pdf |
| Database: | SwePub |
Nájsť tento článok vo Web of Science | Abstract: | We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite Γ1.p1/-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 [A. Caraiani et al., Compos. Math. 156 (2020)]. 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. |
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| ISSN: | 14359863 14359855 |
| DOI: | 10.4171/JEMS/1195 |