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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„Multivariable ($\phi$,$\Gamma$)-modules“
Ass.Prof. Gergely Zábrádi, Eötvös Loránd University, Budapest

The notion of multivariable (phi,Gamma)-modules were introduced recently in order to generalize (parts of) Colmez's work on the p-adic Langlands programme from GL_2(Qp) to groups of higher rank. More specifically: there exists a functor with promising exactness- and compatibility properties from the category of smooth mod p^n representations of the group G of Qp-points of a Qp-split reductive group with connected centre to d-variable (phi,Gamma)-modules where d is the number of simple roots of G. Further, there is a Fontaine-style equivalence of categories between these multivariable objects and p-adic representations of d-fold products of local Galois groups. There is a new proof of this fact using Drinfeld's lemma for perfectoid spaces (jt. with Annie Carter and Kiran S. Kedlaya). In my talk I plan to concentrate on the Galois side of the picture. In part also joint work with Aprameyo Pal.

Freitag, den 7. Juni 2019 um 13:30 Uhr, in INF 205, SR A Freitag, den 7. Juni 2019 at 13:30, in INF 205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Otmar Venjakob