Fargues Lab

Research focus

ERC Advanced Grant · 2016

GeoLocLang

I formulated recently a conjecture that should allow to geometrize the local Langlands correspondence over a non-archimedean local field. This mixes p-adic Hodge theory, the geometric Langlands program and the classical local Langlands correspondence. This conjecture says that given a discrete local Langlands parameter of a reductive group over a local field of equal or unequal characteristic, one should be able to construct a perverse Hecke eigensheaf on the stack of G-bundles on the "curve" I defined and studied in my joint work with Fontaine. I propose to construct, study and establish the basic properties of the geometric objects involved in this conjecture, this stack of G-bundles…

From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.