Queens College CUNY
Irreducibility of limits of Galois representations
Specializing a (Hida) family of cusp forms at weight one may result in a non-classical modular form, whose Galois representation is the p-adic limit of (traces of) Galois representations of the cusp forms in higher weights. A similar situation occurs on GSp(4) when one specializes a p-adic family of cusp forms at weight two. We will discuss Selmer group conditions that guarantee that these limits of Galois representations are irreducible. This serves as an ingredient in modularity results in both contexts.