The Langlands quotient theorem for complex smooth representations of p-adic general linear groups is an important result, which says that there is a bijection from standard modules to irreducible representations given by the cosocle map. It allows for example to deduce the general Langlands correspondence from the cuspidal case, and also to associate Rankin-Selberg local factors to all irreducible representations of this group.
The aim of this project is to develop an analogue (necessarily non naive, already defining the analogue of standard modules is a problem) of this statement in the l-modular setting, with l not p, and to study applications to l-modular local factors and to the l-modular local Langlands correspondences of Vigneras and Emerton-Helm.
Research Team: Robert Kurinczuk (Imperial College London), Nadir Matringe (U of Poitiers), Alberto Mínguez (U of Vienna), Vincent Sécherre (Versailles U)
Periods of Stay: March 14 - 29, 2020, May 10 - 24, 2020, June 3 - 21, 2020 (all stays postponed due to corona virus)