Quebec Mathematical Sciences Colloquium

December 10, 2021 from 14:00 to 15:00 (Montreal/EST time) On location

Stark's Conjectures and Hilbert's 12th Problem

Colloquium presented by Samit Dasgupta (Duke University)

In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory and the special values of L-functions.  The goal of explicit class field theory is to describe the abelian extensions of a ground number field via analytic means intrinsic to the ground field; this question lies at the core of Hilbert's 12th Problem.  Meanwhile, there is an abundance of conjectures on the values of L-functions at certain special points.  Of these, Stark's Conjecture has relevance toward explicit class field theory.  I will describe two recent joint results with Mahesh Kakde on these topics.  The first is a proof of the Brumer-Stark conjecture away from p=2. This conjecture states the existence of certain canonical elements in abelian extensions of totally real fields.  The second is a proof of an exact formula for Brumer-Stark units that has been developed over the last 15 years.  We show that these units together with other easily written explicit elements generate the maximal abelian extension of a totally real field, thereby giving a p-adic solution to the question of explicit class field theory for these fields.


Hybrid | Seats are limited on-site please register here: | Salle 5340, pavillon André-Aisenstadt | Zoom: ID de réunion : 939 8331 3215 Code secret : 096952