Vanishing theorems for Shimura varieties at unipotent level

  • Ana Caraiani

    Imperial College London, UK
  • Daniel R. Gulotta

    University of Oxford, UK; Max Planck Institute for Mathematics, Bonn, Germany
  • Christian Johansson

    Chalmers University of Technology and the University of Gothenburg, Sweden
Vanishing theorems for Shimura varieties at unipotent level cover
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Abstract

We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite -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 . 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.

Cite this article

Ana Caraiani, Daniel R. Gulotta, Christian Johansson, Vanishing theorems for Shimura varieties at unipotent level. J. Eur. Math. Soc. 25 (2023), no. 3, pp. 869–911

DOI 10.4171/JEMS/1195