Reductions of certain semi-stable Galois representations

Abstract: The L-invariant is an important p-adic invariant attached to certain newforms of level Np where N is co-prime to p. They arise most clearly from the study of local p-adic Galois representations, but they influence global phenomena such as trivial zeros of p-adic L-functions and p-adic families. This talk will focus on how the L-invariant, which we will describe, influences the local Galois representation modulo p. History of the general problem of calculating reductions will be provided. The main result is an exact description of the local mod p representation when the L-invariant is sufficiently large in norm. One novel feature of our work is that it allows for unbounded weights, whereas prior descriptions were limited to weight at most p. This is joint work with Brandon Levin and Tong Liu.

number theory

Audience: researchers in the discipline

Boston University Number Theory Seminar

Series comments: The seminar will now meet in CDS 365 (in the new building!). Tea begins at 3:30 in the same room.