Objective
The proposed project concerns p-adic Hodge Theory, a major area of arithmetic algebraic geometry; it owes its existence to the 1968 observation of John Tate that the well-known Hodge decomposition of the singular cohomology of a complex manifold should have a p-adic analogue, in which the singular cohomology is replaced by the p-adic etale cohomology.
There are currently two distinct approaches to the study of this Hodge-Tate decomposition. The first, developed mainly by Bloch, Kato, and Tsuji, uses algebraic K-theory, syntomic complexes, and p-adic vanishing cycles, while the second, more in line with Tate's original ideas, was developed by Faltings using his almost mathematics and purity theorems.
The project will resolve a number of outstanding open problems in the field, including the relation between these distinct methods, the resolution of a 1983 conjecture of Bloch on vanishing cycles, and the development of integral results keeping track of p-torsion. It is a particularly timely moment to carry out such a project as the ER has recently developed a new integral p-adic cohomology theory with Bhatt and Scholze, while the Supervisor has recently put Faltings' machinery on a rigorous base in an extended joint work with Gros.
The conjunction of the complementary backgrounds of the ER and Supervisor will be central to the project. Specifically, the ER's recent work with Bhatt and Scholze, as well as his expertise in K-theory, topological cyclic homology, de Rham--Witt methods, etc., will be merged with the Supervisor's detailed understanding of the aforementioned works of Bloch, Kato, Tsuji, and Faltings. The theories of perfectoid spaces and pro-etale cohomology, as introduced by Scholze, will play a fundamental role.
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.
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.
- natural sciences mathematics pure mathematics arithmetics
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
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.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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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) H2020-MSCA-IF-2015
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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.
91440 Bures Sur Yvette
France
The organization defined itself as SME (small and medium-sized enterprise) at the time the Grant Agreement was signed.
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.