Automorphic p-adic L-functions and regulators

Mini-course 1: Lecture 3 (p-adic families)

18 oct. 2019, 11:00

1h

Salle de réunion (University of Lille)

Orateur

Chris Williams (Imperial College London)

Description

The correct eigenvarieties to be considered in the Shalika setting are constructed using the parabolic subgroup of $\mathrm{GL}(n)$ having Levi subgroup $\mathrm{GL}(n)\times \mathrm{GL}(n)$. After the introduction of these parabolic eigenvarieties the talk is devoted to the study of the local properties of them and the existence of Shalika components. We use such results in order to perform a $p$-adic variation of the distributions obtained in the second lecture. Using the Mellin transform we produce $p$-adic families of $p$-adic $L$-functions.