Skip to main content
European Commission logo
English English
CORDIS - EU research results
CORDIS
CORDIS Web 30th anniversary CORDIS Web 30th anniversary
Content archived on 2024-06-18

Moduli spaces of local G-shtukas

Objective

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.

Fields of science

Not validated

Call for proposal

ERC-2011-StG_20101014
See other projects for this call

Host institution

TECHNISCHE UNIVERSITAET MUENCHEN
EU contribution
€ 832 121,41
Address
Arcisstrasse 21
80333 Muenchen
Germany

See on map

Region
Bayern Oberbayern München, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Ulrike Ronchetti (Ms.)
Principal investigator
Eva Viehmann (Dr.)
Links
Total cost
No data

Beneficiaries (2)