14-18 October 2019
University of Lille
Europe/Paris timezone

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

18 Oct 2019, 11:00
Salle de réunion (University of Lille)

Salle de réunion

University of Lille

Cité Scientifique – Bâtiment M2 59655 Villeneuve d'Ascq Cedex France


Chris Williams (Imperial College London)


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.

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