Companion forms with non-regular weights

Abstract: In general, for an overconvergent p-adic automorphic form of a definite unitary group, there exist other p-adic automorphic forms with possibly different weights which are associated with the same Galois representation (the companion forms). Under the Taylor-Wiles hypothesis, we determine all the companion forms whose associated Galois representations are generic crystalline over p and with Hodge-Tate weights possibly non-regular. This generalizes the result of Breuil-Hellmann-Schraen in regular cases.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar