Project description
Advancing algebraic geometry through homotopy theory
Algebraic geometry explores the intricate structures underlying mathematical objects, but many areas remain constrained by technical limitations. With this in mind, the ERC-funded MOSHOT project aims to unlock the principles of cohomology theories in algebraic and analytic geometry by expanding the foundations of motivic stable homotopy theory. Focusing on homotopy theory and analytic geometry, MOSHOT will push the boundaries of A1-homotopy invariance and explore new perspectives in p-adic and complex geometry. The project’s objectives include establishing a six-functor formalism, investigating the kernel of A1-localisation and developing calculation techniques in unstable motivic homotopy. By connecting algebraic K-theory with p-adic geometry, MOSHOT will transform the study of these fields.
Objective
This project is centered on the field of algebraic geometry and involves homotopy theory and analytic geometry. The overall goal is to unveil the underlying principles of a large variety of cohomology theories in algebraic and analytic geometry and develop robust foundations that facilitate the study of those cohomology theories from the vantage point of homotopy theory. This will be achieved through innovations of motivic stable homotopy theory beyond the current technical limitations of A1-homotopy invariance. In addition, its interdisciplinary perspective will be advanced, especially in relation to p-adic geometry and complex geometry. The research proposal consists of 5 main objectives, which are organically related to each other. The first objective is to establish a six functor formalism, which would be the most important challenge in non-A1-invariant motivic stable homotopy theory. The second objective is to investigate the kernel of the A1-localization and aims to describe it in terms of p-adic or rational Hodge realization, following the principle of trace methods of algebraic K-theory. In particular, in the p-adic context, this will lead to the p-adic rigidity, which will conclusively connect motivic homotopy theory with p-adic geometry. The third objective is to find out the potential of unstable motivic homotopy theory and develop calculation techniques. The forth objective is to establish a general and universal construction of motivic filtration of localizing invariants, such as algebraic K-theory and topological cyclic homology. The last objective is to explore the analogue in complex geometry, which is an interesting unexplored subject that will pave the way for further developments of motivic homotopy theory for a broader range of analytic geometry.
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: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
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
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2024-STG
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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.
1165 KOBENHAVN
Denmark
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.