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arXiv · 2201.06048

Automorphic congruences between torsion cohomological classes

Boyer Pascal
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Abstract

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 $(1,d-1)$.

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Boyer Pascal. 2022-01-16. Automorphic congruences between torsion cohomological classes. https://arxiv.org/abs/2201.06048

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