On the Brumer—Stark conjecture and refinements — Mahesh Kakde (Indian Institute of Science)

Dirichlet’s class number formula relates leading term of the zeta function of a number field at s=0 to various arithmetic invariants including class number formula of the number field. Start, in an attempt to generalise the class number formula, made a series of conjecture relating leading terms of Artin L-functions at s=0 to arithmetic invariants. I will start with formulation of the Stark conjecture. I will then specialise to the special case of Brumer—Stark conjecture. If time permits I will sketch proof of the Brumer—Stark conjecture. This is joint work with Samit Dasgupta.