p-adic Langlands and the Emerton-Gee stack

Informacje na temat projektu

LEGS

Identyfikator umowy o grant: 884596

DOI

10.3030/884596

Data podpisania przez KE 20 Kwietnia 2020

Data rozpoczęcia 1 Października 2020

Data zakończenia 30 Września 2026

Finansowanie w ramach

• EXCELLENT SCIENCE - European Research Council (ERC)

Koszt całkowity

€ 2 195 110,00

Wkład UE

€ 2 195 110,00

Koordynowany przez

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
United Kingdom

Periodic Reporting for period 3 - LEGS (p-adic Langlands and the Emerton-Gee stack)

Okres sprawozdawczy: 2023-10-01 do 2025-03-31

Podsumowanie kontekstu i ogólnych celów projektu

The project is to understand the relationship between the conjectural p-adic Langlands correspondence and the Emerton--Gee stacks. In more down to earth terms, the objective is to classify certain symmetries occurring in number theory in terms of geometric objects.

Prace wykonane od początku projektu do końca okresu sprawozdawczego oraz najważniejsze dotychczasowe rezultaty

Jack Sempliner has been working with the PI on constructing moduli stacks of ordinary Galois representations.We believe that can prove that these stacks are lci, and considering whether we can use them to describe the ordinary cohomology of Shimura varieties.

The PI's book with Matthew Emerton on the Emerton-Gee stacks (on which the project is based) has been completely revised for publication.

The PI has with Matthew Emerton and Eugen Hellmann formulated categorical versions of the p-adic local Langlands correspondence, which will be described in lecture notes for a 2022 IHES summer school.

The PI has with Andrea Dotto and Matthew Emerton proved a categorical p-adic local Langlands correspondence for GL_2(Q_p).

Innowacyjność oraz oczekiwany potencjalny wpływ (w tym dotychczasowe znaczenie społeczno-gospodarcze i szersze implikacje społeczne projektu)

The formulation of a general p-adic local Langlands correspondence in categorical terms is completely new. Until the end of the project the plan is to work on proving more cases of this correspondence, and understanding its connections to other parts of number theory. In particular I hope to understand the correspondence explicitly for GL_2(F) for F a general p-adic field.

picture of the EG stack