1st November: Daniel Puignau

Title: Fitting Ideals in Arithmetic

Abstract: The notion of Fitting ideal was introduced by Hans Fitting, a student of Emmy Noether. These arithmetically well behaved annihilators played an unexpected role in the Mazur-Wiles' proof of the Iwasawa Main Conjecture. They were also recently used in a proof of the Brumer-Stark conjecture away from p=2, by Dasgupta-Kakde, as well as to understand the minus p-part of a Selmer module introduced by Burns-Kurihara-Sano, whose Fitting ideal turns out to be generated by a Stickelberger element. Recent noncommutative extensions of the Fitting ideals have been formulated to gain more insight into Iwasawa theory and algebraic K-theory, particularly into the special values of some Artin L-functions. In this talk, we will introduce the commutative case and prepare the ground for the formulation of some of these recent results.