Alberto Angurel Andrés: Kolyvagin systems and Fitting ideals of Selmer groups of rank 0

Number Theory Seminar: Alberto Angurel Andrés (University of Nottingham)

Kolyvagin systems and Fitting ideals of Selmer groups of rank 0

The Euler and Kolyvagin system machinery cannot be applied directly to study certain Selmer groups carrying important arithmetic information. This is the case of the Selmer groups defined from Selmer structures of 'core rank' 0, like the classical Selmer group of an elliptic curve. The main obstruction is the lack of non-zero Kolyvagin systems associated these Selmer structures. In this talk, I will describe a method to compute the Fitting ideals of these groups using the Kolyvagin systems existing for an auxiliary Selmer structure obtained after relaxing a local condition at certain prime.