Time：14:00-15:00, Wednesday, June 5 2024
Venue：E4-201
Speaker：Lian Duan, ShanghaiTech University
Title：On the irreducibility of low-dimensional geometric Galois representations
Abstract：In this talk, we discuss the irreducibility of compatible systems of certain five-dimensional geometric Galois representations. Using the modularity results of classical cases, we prove that such a compatible system of representations is either irreducible for almost all p, or decompose uniformly as p varies. Our irreducibility result will deduce an algorithm for checking the irreducibility of corresponding Galois representations. Moreover, by applying a result of Cadoret and Tamagawa on the open image theory of monodromy representation, we can spread out the irreducibility among the family of representations induced by the transcendental part of a family of elliptic surfaces. If time allows, I will talk about a concrete example as application of our main result.
