$p$-adic variation via evaluations on the cohomology

Abstract: I will explain a method to construct automorphic $p$-adic $L$-functions and to study the geometry of eigenvarieties. This is based on the construction and study of certain linear 'evaluation' functionals on the cohomology of the relevant arithmetic manifold. We will give more details in the context of the reductive group $GL_{2n}$ where this methods was applied successfully. This talk is based on joint work with C. Williams and joint work with M. Dimitrov and C. Williams.

number theoryrepresentation theory

Audience: researchers in the topic

Number Theory and Representations in Valparaiso