Modular galois realizations of linear groups

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Project 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)

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Participants

• UNIVERSITAT DE BARCELONA · BARCELONACoordinatorSpain

Links

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