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Multivariate (phi, Gamma)-modules

Speaker: Kiran Kedlaya

Date: Thu, May 18, 2017

Location: PIMS, University of British Columbia

Conference: Focus Period on Representations in Arithmetic

Subject: Mathematics, Number Theory

Class: Scientific

Abstract:

The classical theory of (phi, Gamma)-modules relates continuous p-adic representations of the Galois group of a p-adic field with modules over a certain mildly noncommutative ring. That ring admits a description in terms of a group algebra over Z_p which is crucial for Colmez's p-adic local Langlands correspondence for GL_2(Q_p). We describe a method for applying a key property of perfectoid spaces, the analytic analogue of Drinfeld's lemma, to the construction of "multivariate (phi, Gamma)-modules" corresponding to p-adic Galois representations in more exotic ways. Based on joint work with Annie Carter and Gergely Zabradi.