On the Brumer-Stark conjecture and refinements

Abstract: In this talk I will describe my recent work with Mahesh Kakde on the Brumer-Stark Conjecture and certain refinements. I will give a broad overview that motivates the conjecture and gives connections to explicit class field theory. I will conclude with a description of recent work (joint w/ Kakde, Jesse Silliman, and Jiuya Wang) in which we complete the proof of the conjecture. Moreover, we deduce a certain special case of the Equivariant Tamagawa Number Conjecture, which has important corollaries. The key aspect of the most recent results, which allows us to handle the prime $p=2$, is the proof of a version of Ribet's Lemma in the case of characters that are congruent modulo $p$.

number theory

Audience: researchers in the topic

BC-MIT number theory seminar