Cristian Popescu (University of California)
Title: Equivariant Iwasawa theory for Artin motives and applications
Abstract:聽 Several years ago, Greither and I formulated and gave a聽conditional proof聽聽of an Equivariant Main Conjecture (EMC) in Iwasawa theory for Artin motives over arbitrary global fields. We showed that, via Iwasawa codescent, this statement implies strong versions of the Brumer-Stark and Coates-Sinnott conjectures concerning special values of equivariant聽 Artin L-functions at non-positive integers.聽
In this lecture, I will describe my recent joint work with Rusiru Gambheera, in which we give聽unconditional proofs聽of two new versions of the EMC: one involving the Selmer modules of Burns-Kurihara-Sano and the other involving the Ritter-Weiss modules. I will then relate these results to my earlier work with Greither and discuss their applications to proving various conjectures聽
on special values of equivariant Artin L-functions. These advances rely crucially on the recent breakthrough results of Dasgupta and Kakde on Hilbert's twelfth problem for totally real number fields.