Objetivo 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. Ámbito científico natural sciencesmathematicspure mathematicsgeometry Programa(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) Tema(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Convocatoria de propuestas ERC-2011-StG_20101014 Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-SG - ERC Starting Grant Institución de acogida TECHNISCHE UNIVERSITAET MUENCHEN Aportación de la UE € 832 121,41 Dirección Arcisstrasse 21 80333 Muenchen Alemania Ver en el mapa Región Bayern Oberbayern München, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Ulrike Ronchetti (Ms.) Investigador principal Eva Viehmann (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos Beneficiarios (2) Ordenar alfabéticamente Ordenar por aportación de la UE Ampliar todo Contraer todo TECHNISCHE UNIVERSITAET MUENCHEN Alemania Aportación de la UE € 832 121,41 Dirección Arcisstrasse 21 80333 Muenchen Ver en el mapa Región Bayern Oberbayern München, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Ulrike Ronchetti (Ms.) Investigador principal Eva Viehmann (Dr.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN La participación finalizó Alemania Aportación de la UE € 67 878,59 Dirección REGINA PACIS WEG 3 53113 Bonn Ver en el mapa Región Nordrhein-Westfalen Köln Bonn, Kreisfreie Stadt Tipo de actividad Higher or Secondary Education Establishments Contacto administrativo Daniela Hasenpusch (Ms.) Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Coste total Sin datos
