Companion forms and partially classical eigenvarieties

Abstract: In general, there exist $p$-adic automorphic forms of different weights with the same associated $p$-adic Galois representation. In this talk, I will report some result on the existence of companion forms for definite unitary groups when the Hodge-Tate weights are not regular, generalizing the work of Breuil-Hellmann-Schraen in regular cases. One key ingredient of the proof is some partially classical properties of $p$-adic automorphic forms in the term of Emerton's Jacquet module for locally analytic representations, which will imply some partially de Rham properties of Galois representations in finite slope cases with the help of Ding's partial eigenvarieties.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar