Moduli spaces of local G-shtukas

Projektinformationen

G-SHTUKAS

ID Finanzhilfevereinbarung: 277889

Projekt abgeschlossen

Startdatum 1 September 2011

Enddatum 28 Februar 2017

Finanziert unter

• Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Gesamtkosten € 900 000,00

EU-Beitrag € 900 000,00

Koordiniert durch

TECHNISCHE UNIVERSITAET MUENCHEN
Germany

Ziel

This project provides a novel approach to the local Langlands programme via a comprehensive investigation of local G-shtukas and their moduli spaces and the exploitation of their relations to Shimura varieties.

Local G-shtukas are generalisations to arbitrary reductive groups of the local analogue of Drinfeld shtukas. They also are the function field counterpart of p-divisible groups. Hence moduli spaces of local G-shtukas are of great interest, in particular for the geometric realisation of local Langlands correspondences. Compared to p-divisible groups local G-shtukas have several advantages. They can be defined and studied for any reductive group, enabling a systematic use of group theoretic methods and promising unified results. Furthermore, their local description by elements of loop groups makes them more accessible than the description of p-divisible groups by Cartier theory or displays. Comparison theorems to p-divisible groups then provide a novel way to insight into their moduli spaces.

The research plan of this project is subdivided into three strands which mutually benefit from each other: Firstly we want to understand the representations realised in the cohomology of moduli spaces of local G-shtukas in connection with the geometric local Langlands programme. Secondly, we study the geometry of the moduli spaces and investigate several natural stratifications. Finally, we build the bridge to Shimura varieties. On the one hand we explore the source of new results obtained by transferring methods developed for one of the two sides (Shimura varieties resp. moduli spaces of local G-shtukas) to prove similar assertions for the other. On the other hand we establish closer ties by proving direct comparison theorems.

Wissenschaftliches Gebiet

• natural sciences › mathematics › pure mathematics › geometry

Programm/Programme

• FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Thema/Themen

• ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations

Aufforderung zur Vorschlagseinreichung

ERC-2011-StG_20101014
Andere Projekte für diesen Aufruf anzeigen

Finanzierungsplan

ERC-SG - ERC Starting Grant

Gastgebende Einrichtung

TECHNISCHE UNIVERSITAET MUENCHEN

Kontakt Verwaltung

Ulrike Ronchetti (Ms.)

Hauptforscher

Eva Viehmann (Dr.)

• EU-Beitrag: € 832 121,41
• Adresse: Arcisstrasse 21 ; 80333 Muenchen ; Deutschland
• Region: Bayern › Oberbayern › München, Kreisfreie Stadt
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten

Begünstigte (2)

TECHNISCHE UNIVERSITAET MUENCHEN

Deutschland

Kontakt Verwaltung

Ulrike Ronchetti (Ms.)

Hauptforscher

Eva Viehmann (Dr.)

• EU-Beitrag: € 832 121,41
• Adresse: Arcisstrasse 21 ; 80333 Muenchen
• Region: Bayern › Oberbayern › München, Kreisfreie Stadt
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten

RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN

Beteiligung beendet

Deutschland

Kontakt Verwaltung

Daniela Hasenpusch (Ms.)

• EU-Beitrag: € 67 878,59
• Adresse: REGINA PACIS WEG 3 ; 53113 Bonn
• Region: Nordrhein-Westfalen › Köln › Bonn, Kreisfreie Stadt
• Aktivitätstyp: Higher or Secondary Education Establishments
• Gesamtkosten: Keine Daten