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GMLP SIGNED

Global Methods in the Langlands Program

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EC-Contrib. €

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Project "GMLP" data sheet

The following table provides information about the project.

Coordinator
THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE 

Organization address
address: TRINITY LANE THE OLD SCHOOLS
city: CAMBRIDGE
postcode: CB2 1TN
website: www.cam.ac.uk

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Project website https://www.dpmms.cam.ac.uk/
 Total cost 1˙094˙610 €
 EC max contribution 1˙094˙610 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-01-01   to  2021-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE CHANCELLOR MASTERS AND SCHOLARSOF THE UNIVERSITY OF CAMBRIDGE UK (CAMBRIDGE) coordinator 1˙094˙610.00

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 Project objective

The Langlands program is a conjectural framework for understanding the deep relations between automorphic forms and arithmetic. It implies a parameterization of representations of Galois groups of (local or global) fields in terms of representations of (p-adic or adelic) reductive groups. While making progress in the Langlands program often means overcoming significant technical obstacles, new results can have concrete applications to number theory, the proof of Fermat's Last Theorem by Wiles being a key example.

Recently, V. Lafforgue has made a striking breakthrough in the Langlands program over function fields, by constructing an `automorphic-to-Galois' Langlands correspondence. As a consequence, this should imply the existence of a local Langlands correspondence over equicharacteristic non-archimedean local fields.

The goal of this proposal is to show the surjectivity of this local Langlands correspondence. My strategy will be global, and will involve solving global problems of strong independent interest. I intend to establish a research group to carry out the following objectives, in the setting of global function fields:

I. Establish automorphy lifting theorems for Galois representations valued in the (Langlands) dual group of an arbitrary split reductive group. II. Establish cases of automorphic induction for arbitrary reductive groups. III. Prove potential automorphy theorems for Galois representations valued in the dual group of an arbitrary reductive group. IV. Establish cases of soluble base change and descent for automorphic representations of arbitrary reductive groups. I will then combine these results to obtain the desired surjectivity. This will be a milestone in our understanding of the Langlands correspondence for function fields.

 Publications

year authors and title journal last update
List of publications.
2020 Johansson, Christian; Thorne, Jack A.
On subquotients of the etale cohomology of Shimura varieties
published pages: , ISSN: , DOI:
\"\"\"Shimura Varieties\"\" in London Mathematical Society Lecture Note Series\" 457 2020-03-05
2019 Gebhard Böckle, Michael Harris, Chandrashekhar Khare, Jack A. Thorne
$hat{G}$-local systems on smooth projective curves are potentially automorphic
published pages: 1-111, ISSN: 0001-5962, DOI: 10.4310/acta.2019.v223.n1.a1
Acta Mathematica 223/1 2020-03-05
2019 Jack A. Thorne
On the average number of 2-Selmer elements of elliptic curves over F_q(X) with two marked points
published pages: , ISSN: 1431-0635, DOI: 10.25537/dm.2019v24.1179-1223
Documenta Mathematica 2020-03-05

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