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Fargues' conjecture in the GL_2-case


Hold Date 2019-01-15 16:00~2019-01-15 17:00

Place Lecture Room M W1-C-512, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Ildar Gaisin (The University of Tokyo)

Abstract:
Recently Fargues announced a conjecture which attempts to geometrize the (classical) local Langlands correspondence. Just as in the geometric Langlands story, there is a stack of G-bundles and a Hecke stack which one can define. The conjecture is based on some conjectural objects, however for a cuspidal Langlands parameter and a minuscule cocharacter, we can define every object in the conjecture, assuming only the local Langlands correspondence. We study the geometry of the non-semi-stable locus in the Hecke stack and as an application we will show the Hecke eigensheaf property of Fargues conjecture holds in the GL_2-case and a cuspidal Langlands parameter. This is joint work with Naoki Imai.