p-adic Langlands and the Emerton-Gee stack

Informazioni relative al progetto

LEGS

ID dell’accordo di sovvenzione: 884596

DOI

10.3030/884596

Data della firma CE 20 Aprile 2020

Data di avvio 1 Ottobre 2020

Data di completamento 30 Settembre 2026

Finanziato da

• EXCELLENT SCIENCE - European Research Council (ERC)

Costo totale

€ 2 195 110,00

Contributo UE

€ 2 195 110,00

Coordinato da

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
United Kingdom

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

Periodo di rendicontazione: 2023-10-01 al 2025-03-31

Sintesi del contesto e degli obiettivi generali del progetto

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.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

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).

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

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