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# FROM LOCAL TO GLOBAL CONGRUENCES FOR AUTOMORPHIC REPRESENTATIONS

Abstract : Given a irreducible automorphic representation $\Pi$ of a similitude group $G/\mathbb Q$ giving rise to a KHT-Shimura variety, given a local congruence of the local component of $\Pi$ at a fixed place $p$, we justify the existence of a global automorphic representation $\Pi'$ with the same weight and the same level outside $p$ than $\Pi$, such that $\Pi$ and $\Pi'$ are weakly congruent. The arguments rest on the separation of the various contributions coming either from torsion or on the distinct families of automorphic representations, to the modulo $l$ reduction of the cohomology of Harris-Taylor perverse sheaves.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03527658
Contributor : Pascal Boyer Connect in order to contact the contributor
Submitted on : Sunday, January 16, 2022 - 2:31:01 PM
Last modification on : Tuesday, January 18, 2022 - 3:38:16 AM
Long-term archiving on: : Sunday, April 17, 2022 - 6:07:14 PM

### File

congruence-torsion.pdf
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### Identifiers

• HAL Id : hal-03527658, version 1

### Citation

Pascal Boyer. FROM LOCAL TO GLOBAL CONGRUENCES FOR AUTOMORPHIC REPRESENTATIONS. 2022. ⟨hal-03527658⟩

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