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ModRed SIGNED

The geometry of modular representations of reductive algebraic groups

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EC-Contrib. €

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Project "ModRed" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITE CLERMONT AUVERGNE 

Organization address
address: 49 BOULEVARD FRANCOIS MITTERRAND
city: CLERMONT-FERRAND
postcode: 63000
website: http://creation-uca.fr/

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 France [FR]
 Total cost 882˙843 €
 EC max contribution 882˙843 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE CLERMONT AUVERGNE FR (CLERMONT-FERRAND) coordinator 710˙718.00
2    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) participant 172˙125.00

Map

 Project objective

The main theme of this proposal is the Geometric Representation Theory of reductive algebraic groups over algebraically closed fields of positive characteristic. Our primary goal is to obtain character formulas for simple and for indecomposable tilting representations of such groups, by developing a geometric framework for their categories of representations. Obtaining such formulas has been one of the main problems in this area since the 1980's. A program outlined by G. Lusztig in the 1990's has lead to a formula for the characters of simple representations in the case the characteristic of the base field is bigger than an explicit but huge bound. A recent breakthrough due to G. Williamson has shown that this formula cannot hold for smaller characteristics, however. Nothing is known about characters of tilting modules in general (except for a conjectural formula for some characters, due to Andersen). Our main tools include a new perspective on Soergel bimodules offered by the study of parity sheaves (introduced by Juteau-Mautner-Williamson) and a diagrammatic presentation of their category (due to Elias-Williamson).

 Publications

year authors and title journal last update
List of publications.
2018 Riche , Simon; Williamson , Geordie
Tilting modules and the p-canonical basis
published pages: 1-184, ISSN: 0303-1179, DOI:
Astérisque 397 2019-07-08
2019 Pramod N. Achar, Simon Riche
Reductive groups, the loop Grassmannian, and the Springer resolution
published pages: 289-436, ISSN: 0020-9910, DOI: 10.1007/s00222-018-0805-1
Inventiones mathematicae 214 2019-07-08
2019 Pramod N. Achar, Shotaro Makisumi, Simon Riche, Geordie Williamson
Koszul duality for Kac–Moody groups and characters of tilting modules
published pages: 261-310, ISSN: 0894-0347, DOI: 10.1090/jams/905
Journal of the American Mathematical Society 32/1 2019-04-18
2018 Achar , Pramod ,; Cooney , Nicholas; Riche , Simon
The parabolic exotic t-structure
published pages: , ISSN: 2491-6765, DOI:
Epijournal de Géométrie Algébrique 2 2019-04-18
2018 Carl Mautner, Simon Riche
Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković–Vilonen conjecture
published pages: 2259-2332, ISSN: 1435-9855, DOI: 10.4171/jems/812
Journal of the European Mathematical Society 20/9 2019-04-18

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