Description

Speaker: Aditya Karnataki

Date and time: Wednesday, April 20th at 11.30

Title : Families of (φ, τ)-modules and Galois representations

Abstract : Let K be a finite extension of ℚp. The theory of (φ, Γ)-modules constructed by Fontaine provides a good category to study p-adic representations of the absolute Galois group Gal(K/K). This theory arises from a ``devissage'' of the extension K/K through an intermediate extension K∞/K which is the cyclotomic extension of K. The notion of (φ, τ)-modules generalizes Fontaine's constructions by using Kummer extensions other than the cyclotomic one. It encapsulates the important notion of Breuil-Kisin modules among others. It is thus desirable to establish properties of (φ, τ)-modules parallel to the cyclotomic case. In this talk, we explain the construction of a functor that associates to a family of p-adic Galois representations a family of (φ, τ)-modules. The analogous functor in the (φ, Γ)-modules case was constructed by Berger and Colmez . This is joint work with Léo Poyeton.

Date and time: Wednesday, April 20th at 11.30

Title : Families of (φ, τ)-modules and Galois representations

Abstract : Let K be a finite extension of ℚp. The theory of (φ, Γ)-modules constructed by Fontaine provides a good category to study p-adic representations of the absolute Galois group Gal(K/K). This theory arises from a ``devissage'' of the extension K/K through an intermediate extension K∞/K which is the cyclotomic extension of K. The notion of (φ, τ)-modules generalizes Fontaine's constructions by using Kummer extensions other than the cyclotomic one. It encapsulates the important notion of Breuil-Kisin modules among others. It is thus desirable to establish properties of (φ, τ)-modules parallel to the cyclotomic case. In this talk, we explain the construction of a functor that associates to a family of p-adic Galois representations a family of (φ, τ)-modules. The analogous functor in the (φ, Γ)-modules case was constructed by Berger and Colmez . This is joint work with Léo Poyeton.

Description

Ramanujan Hall, Department of Mathematics

Date

Wed, April 20, 2022

Start Time

11:30am IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Tue, April 19, 2022 11:13am IST