$p$-Local indecomposability of non-CM modular $p$-adic Galois representations and the structure of Hecke algebras

Abstract: A conjecture by R. Greenberg asserts that a modular 2-dimensional $p$-adic Galois representation of a cusp form of weight larger than or equal to 2 is indecomposable over the $p$-inertia group unless it is induced from an imaginary quadratic field. I start with a survey of the known results and try to reach a brief description of new cases of indecomposability.

number theoryrepresentation theory

Audience: researchers in the topic

Number Theory and Representations in Valparaiso