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 natural sciencesmathematicspure mathematicsgeometry Programme(s) 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) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2011-StG_20101014 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Coordinator TECHNISCHE UNIVERSITAET MUENCHEN 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 Contact the organisation Opens in new window Website Opens in new window EU contribution € 832 121,41 Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all TECHNISCHE UNIVERSITAET MUENCHEN Germany EU contribution € 832 121,41 Address Arcisstrasse 21 80333 Muenchen 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 Contact the organisation Opens in new window Website Opens in new window RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN Participation ended Germany EU contribution € 67 878,59 Address Regina pacis weg 3 53113 Bonn See on map Region Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Activity type Higher or Secondary Education Establishments Administrative Contact Daniela Hasenpusch (Ms.) Links Contact the organisation Opens in new window Website Opens in new window
