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arXiv · 1910.09214

Vanishing theorems for Shimura varieties at unipotent level

Ana Caraiani·Daniel R. Gulotta·Christian Johansson
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Abstract

We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite $Γ_1(p^\infty)$-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 $Γ_1(p^\infty)$ 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.

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BibTeXRIS

Ana Caraiani, Daniel R. Gulotta, Christian Johansson. 2021-07-05. Vanishing theorems for Shimura varieties at unipotent level. https://doi.org/10.4171/jems%2F1195

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