Jean-Louis Colliot-Thélène, CNRS
and Paris-Saclay University (Orsay)
December 11th, 2020 2:30-3:30 pm CET
Title : Jumps in the rank of the Mordell-Weil group
Abstract : Let be a number field and a smooth integral -variety. Let → be an abelian scheme. We consider the set ⊂ of -rational points of such that the Mordell-Weil rank of the fibre is strictly bigger than the Mordell-Weil rank of the generic fibre over the function field .
We prove : if the -variety is -unirational, then is dense for the Zariski topology on . Variants are given and compared with old and new results in the literature.