1. From local to global congruences for automorphic representations
- Author
-
Boyer, Pascal
- Subjects
Mathematics::Algebraic Geometry ,Mathematics - Number Theory ,Mathematics::Number Theory ,FOS: Mathematics ,Number Theory (math.NT) ,Mathematics::Representation Theory - 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., Comment: 3 figures
- Published
- 2022