Objective
The aim of the proposed research is to study the homotopy theory of algebraic varieties and other algebraically defined geometric objects, especially over fields other than the complex numbers. A noticeable emphasis will be put on fundamental groups and on K(pi, 1) spaces, which serve as building blocks for more complicated objects. The most important source of both motivation and methodology is my recent discovery of the K(pi, 1) property of affine schemes in positive characteristic and its relation to wild ramification phenomena.
The central goal is the study of etale homotopy types in positive characteristic, where we hope to use the aforementioned discovery to yield new results beyond the affine case and a better understanding of the fundamental group of affine schemes. The latter goal is closely tied to Grothendieck's anabelian geometry program, which we would like to extend beyond its usual scope of hyperbolic curves.
There are two bridges going out of this central point. The first is the analogy between wild ramification and irregular singularities of algebraic integrable connections, which prompts us to translate our results to the latter setting, and to define a wild homotopy type whose fundamental group encodes the category of connections.
The second bridge is the theory of perfectoid spaces, allowing one to pass between characteristic p and p-adic geometry, which we plan to use to shed some new light on the homotopy theory of adic spaces. At the same time, we address the related question: when is the universal cover of a p-adic variety a perfectoid space? We expect a connection between this question and the Shafarevich conjecture and varieties with large fundamental group.
The last part of the project deals with varieties over the field of formal Laurent series over C, where we want to construct a Betti homotopy realization using logarithmic geometry. The need for such a construction is motivated by certain questions in mirror symmetry.
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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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.1.1. - EXCELLENT SCIENCE - 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.
ERC-STG - Starting Grant
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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-2018-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.
00-656 Warszawa
Poland
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.