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GeoLocLang

Objective

"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 being a ""perfectoid stacks"" in the framework of Scholze theory of perfectoid spaces. At the same time I propose to establish the first steps in the proof of this conjecture, study particular cases in more details and explore consequences of this conjecture."

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Net EU contribution
€ 1 301 863,00
Address
Rue Michel Ange 3
75794 Paris
France

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Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Non-EU contribution
€ 0,00

Beneficiaries (1)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
Net EU contribution
€ 1 301 863,00
Address
Rue Michel Ange 3
75794 Paris

See on map

Region
Ile-de-France Ile-de-France Paris
Activity type
Research Organisations
Non-EU contribution
€ 0,00