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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."

Call for proposal

ERC-2016-ADG
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Funding Scheme

ERC-ADG - Advanced Grant

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU contribution
€ 1 301 863

Beneficiaries (1)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
EU contribution
€ 1 301 863
Address
Rue Michel Ange 3
75794 Paris
Activity type
Research Organisations