BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Slopes of modular form and ghost conjecture
Slopes of modular form and ghost conjecture
Organizers
Hansheng Diao , Yueke Hu , Emmanuel Lecouturier , Cezar Lupu
Speaker
Bin Zhao
Time
Tuesday, November 1, 2022 4:00 PM - 5:00 PM
Venue
1131
Online
Zoom 293 812 9202 (BIMSA)
Abstract
In 2016, Bergdall and Pollack raised a conjecture towards the computation of the p-adic slopes of Hecke cuspidal eigenforms whose associated p-adic Galois representations satisfy the assumption that their mod p reductions become reducible when restricted to the p-decomposition group. In this talk, I will report the joint work with Ruochuan Liu, Nha Truong and Liang Xiao to prove this conjecture under mild assumptions. I will start with the statement of this conjecture and the intuition behind it. Then I will explain some strategies of our proof. If time permits, I will mention some arithmetic applications of this conjecture.