Skip to main content
Go to the home page of the European Commission (opens in new window)
English English
CORDIS - EU research results
CORDIS

Motives and the Langlands program

Objective

This proposal belongs to the field of arithmetic geometry and lies at the interface of number theory, algebraic geometry and the theory of automorphic forms. More precisely, I aim to use algebraic cycles in the form of motivic sheaves to address fundamental questions about the Langlands program for function fields. This aims at motivic Langlands parametrizations. The Langlands program predicts a decomposition of the space of automorphic forms by motivic Langlands parameters. A breakthrough of V. Lafforgue for function fields with generalizations by Xue, Zhu, Drinfeld and Gaitsgory led to tremendous progress in the construction of l-adic Langlands parameters. The recent work of Fargues--Scholze for non-Archimedean local fields uses similar techniques in another context. This should be viewed as the l-adic realization of the conjectured motivic parametrization. Independently, recent advances for motivic sheaves, as envisioned by Grothendieck and realized by Voevodsky, Ayoub, Cisinski--Dglise, provide powerful techniques to handle algebraic cycles. Despite the immense progress in both areas, hardly any advances have been made specifying the motivic nature of Langlands original prediction. My project aims to develop new tools to make motivic sheaves amenable for applications in the Langlands program for function fields. In my ongoing joint work with Scholbach, we have successfully implemented key constructions such as IC-Chow groups of shtuka spaces and the motivic Satake equivalence (Math. Ann.) bypassing the use of standard conjectures on algebraic cycles. As in my joint work with Haines, this in particular requires to study the geometry of infinite dimensional varieties such as the affine Grassmannian. Based on these results, I will attack the longstanding open problem on the relation of automorphic forms and motives in the function field case.

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.

You need to log in or register to use this function

Keywords

Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)

Programme(s)

Multi-annual funding programmes that define the EU’s priorities for research and innovation.

Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

HORIZON-ERC - HORIZON ERC Grants

See all projects funded under this funding scheme

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

(opens in new window) ERC-2021-STG

See all projects funded under this call

Host institution

TECHNISCHE UNIVERSITAT DARMSTADT
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 1 409 163,00
Address
KAROLINENPLATZ 5
64289 Darmstadt
Germany

See on map

Region
Hessen Darmstadt Darmstadt, Kreisfreie Stadt
Activity type
Higher or Secondary Education Establishments
Links
Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 1 409 163,00

Beneficiaries (1)

My booklet 0 0