Objective
"Galois representations have become one of the central objects of study in number theory and arithmetic geometry. Since Wiles' proof of the Taniyama-Shimura conjecture (hence the completion of the proof of Fermat's last theorem) using Iwasawa theoretical ideas (via Hida's and Mazur's theory of deformations of Galois representations), tremendous amount of progress have been made in the study of Galois representations. Despite the great achievements in the last decade, many important questions in this area of research remain open, such as the ""main conjectures"" of Iwasawa theory in various contexts, posed in great generality by Greenberg, for various Galois representations and for their various deformations. Once the main conjectures are proven, many interesting arithmetic data may be extracted about the Galois representation one starts off with. The main technical tool to attack the main conjectures is the machinery of Euler systems and Kolyvagin systems. This project aims for a study of Euler systems and Kolyvagin systems attached to Galois representations and attached to their Iwasawa theoretical deformations; as well as related themes within the Euler system theory. Some progress have already been made by the applicant in his thesis where he was able to prove that Kolyvagin systems attached to many Galois representations could be deformed along the ""cyclotomic direction"", namely in the most classical Iwasawa theoretical setting. Currently, he is involved with a relevant project about the construction of Kolyvagin systems for the nearly ordinary deformations of Galois representations attached to Hilbert modular forms, out of Euler systems constructed by Olivier Fouquet in his thesis. Should this project succeed, it already would be an important step further beyond the treatment of Mazur-Rubin and the applicant's thesis, where they have successfully dealt with the Kolyvagin system theory for the ""cyclotomic"" deformations, namely the simplest type."
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
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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)
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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.
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.
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.
FP7-PEOPLE-IRG-2008
See other projects for this call
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.
Coordinator
34450 Istanbul
Türkiye
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.