Title: Eigenvarieties and a conjecture of Urban
Speaker: Glenn Stevens
Speaker Info: Boston University
Special Note: In a separate talk (2:00-2:45 pm in 101 Annenberg Hall) for graduate students and non-specialists, the speaker will discuss explicit concrete examples from the classical theory of modular forms in the spirit of Hida and Coleman.
Eigenvarieties have played an important role in the p-adic theory of automorphic forms and their global arithmetic properties, by providing a natural context for investigating families of galois representations, and p-adic L-functions. In this talk we present an axiomatic construction of cohomological eigenvarieties and discuss a conjecture of Eric Urban that predicts the dimension of these eigenvarieties in automorphic settings. Our starting point is the “eigenvariety machine” of Coleman-Mazur and Buzzard which produces eigenvarieties attached to orthonormalizable Banach modules with an action of the Hecke algebra. We extend this by constructing eigenvarieties associated to the arithmetic cohomology of orthonormalizable Banach modules and by giving a lower bound for their dimensions. These results are based on joint work with Avner Ash.Date: Monday, November 14, 2011