Big Galois image for p-adic families of finite slope modular forms.
Abstract:
I present the result of a joint work with A. Iovita and J. Tilouine. We study the image of the Galois representation associated with a p-adic family of modular forms of finite positive slope. We prove that this image is big, in a precise sense, and that its size can be described in terms of the congruences of the family with overconvergent CM eigenforms. These results are analogous to those obtained by H. Hida and J. Lang for ordinary families.e modular forms.