Colloquium abstracts

J. Tilouine
Universite Paris, France
July 9, 2015

Big image of Galois for positive slope families:  In the 90's, Coleman and Mazur defined the Eigencurve $X$ which parametrizes the Hecke eigensystems of modular forms with non zero eigenvalue for $U_p$. Recently, Hida showed that non CM ordinary families have big Galois image. We do the same, in the non ordinary case, for families of finite slope on $X$. The ingredient replacing ordinarity is Sen's theory in the relative setting.