Objetivo The Langlands program is a conjectural framework for understanding the deep relations between automorphic forms and arithmetic. It implies a parameterization of representations of Galois groups of (local or global) fields in terms of representations of (p-adic or adelic) reductive groups. While making progress in the Langlands program often means overcoming significant technical obstacles, new results can have concrete applications to number theory, the proof of Fermat's Last Theorem by Wiles being a key example.Recently, V. Lafforgue has made a striking breakthrough in the Langlands program over function fields, by constructing an `automorphic-to-Galois' Langlands correspondence. As a consequence, this should imply the existence of a local Langlands correspondence over equicharacteristic non-archimedean local fields.The goal of this proposal is to show the surjectivity of this local Langlands correspondence. My strategy will be global, and will involve solving global problems of strong independent interest. I intend to establish a research group to carry out the following objectives, in the setting of global function fields:I. Establish automorphy lifting theorems for Galois representations valued in the (Langlands) dual group of an arbitrary split reductive group.II. Establish cases of automorphic induction for arbitrary reductive groups.III. Prove potential automorphy theorems for Galois representations valued in the dual group of an arbitrary reductive group.IV. Establish cases of soluble base change and descent for automorphic representations of arbitrary reductive groups.I will then combine these results to obtain the desired surjectivity. This will be a milestone in our understanding of the Langlands correspondence for function fields. Ámbito científico social sciencespolitical sciencespolitical policiescivil societynongovernmental organizationsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsarithmeticsprime numbersnatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programa(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Tema(s) ERC-2016-STG - ERC Starting Grant Convocatoria de propuestas ERC-2016-STG Consulte otros proyectos de esta convocatoria Régimen de financiación ERC-STG - Starting Grant Institución de acogida THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Aportación neta de la UEn € 1 094 610,00 Dirección TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge Reino Unido Ver en el mapa Región East of England East Anglia Cambridgeshire CC Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 094 610,00 Beneficiarios (1) Ordenar alfabéticamente Ordenar por aportación neta de la UE Ampliar todo Contraer todo THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Reino Unido Aportación neta de la UEn € 1 094 610,00 Dirección TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge Ver en el mapa Región East of England East Anglia Cambridgeshire CC Tipo de actividad Higher or Secondary Education Establishments Enlaces Contactar con la organización Opens in new window Sitio web Opens in new window Participación en los programas de I+D de la UE Opens in new window Red de colaboración de HORIZON Opens in new window Coste total € 1 094 610,00
