Summary
"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."
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."
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| Web resources: | https://cordis.europa.eu/project/id/742608 |
| Start date: | 01-10-2017 |
| End date: | 31-03-2023 |
| Total budget - Public funding: | 1 301 863,00 Euro - 1 301 863,00 Euro |
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Original description
"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."
Status
SIGNEDCall topic
ERC-2016-ADGUpdate Date
27-04-2024
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