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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.06048 |
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Table of Contents:
- For two representations of some local division algebra, congruent modulo $l$, giving rise to two Harris-Taylor local systems on the corresponding Newton strata of the special fiber of a KHT Shimura varieties, we prove that the $l$-torsion of each of their cohomology groups with compact supports are isomorphic, or equivalently the free quotients of each of the cohomology groups are congruent modulo $l$. We then deduce the construction of accurate non tempered automorphic congruences for a similitude group $G/\mathbb Q$ with signature $(1,d-1)$.