On the Root of Unity Ambiguity in a Formula for the Brumer--Stark Units

Abstract

We prove a conjectural formula for the Brumer--Stark units. Dasgupta--Kakde have shown the formula is correct up to a bounded root of unity. In this paper we resolve the ambiguity in their result. We also remove an assumption from Dasgupta--Kakde's result on the formula.

12 pages. This version proves a stronger result, dealing with the ambiguity at 2