Objective
Research objectives and content
The objective is to obtain new families of linear groups over finite fields realized as Galois groups over the rationals by considering Galois representations attached to abelian varieties with large endomorphism rings, and giving conditions for these representations to have images as large as possible. Ribet has recently shown that the jacobian of a modular curve fulfills these conditions, so that by studying the ring of Hecke operators in these varieties one can obtain Galois realizations. In the 3-dimensional case, based on Ash's conjecture and the experimental indications that support it, we will try to construct more examples of Galois representations 'seeming to be attached' to Hecke eigenclass (in the mod 'ro' cohomology of a congruence subgroup of SL3 (><), specially those with image as large as possible. We will also try to generalize to this case some techniques usually applied in dimension two.
Training content (objective, benefit and expected impact)This training will allow me to complete my PhD working in my field. Through this training I will develop the skills necessary to work as researcher.
Links with indusuy / industrial relevance (22)
Fields of science (EuroSciVoc)
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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.
Topic(s)
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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
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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
08007 BARCELONA
Spain
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.