seminar: Recent progress on a uniform version of Serre's open image theorem

speaker: Loïc Merel (Université de Paris VII)

abstract: A theorem of J-P. Serre asserts that any automorphism on the p-division points of a (non-CM) elliptic curve over Q comes from an element of the Galois group, when p is a large enough prime number. A uniform version would assert that the "large enough" does not depend on the elliptic curve, for instance p>37. It is classical to decompose this problem in terms of rational points on modular curves associated to the maximal subgroups of GL₂(F_p) : Borel subgroups, normalizer of split Cartan subgroups, normalizer of nonsplit Cartan subgroups. The case of Borel subgroups has been treated by B. Mazur in the 1970's. I will discuss the recent progress on the normalizer of split Cartan case due to P. Parent and M. Rebolledo.

timetable:
Tue 19 Apr, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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