December 10, 2021
December 10, 2021 from 14:00 to 15:00 (Montreal/EST time) On location
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.
AddressHybrid | Seats are limited on-site please register here: https://www.eventbrite.ca/e/inscription-csmq-decembre-2021-december-215934143837 | Salle 5340, pavillon André-Aisenstadt | Zoom: https://umontreal.zoom.us/j/93983313215?pwd=clB6cUNsSjAvRmFMME1PblhkTUtsQT09 ID de réunion : 939 8331 3215 Code secret : 096952