On non-abelian Stark-type conjectures

Abstract

We introduce non-abelian generalizations of Brumer's conjecture, the Brumer-Stark conjecture and the strong Brumer-Stark property attached to a Galois CM-extension of number fields. Moreover, we discuss how they are related to the equivariant Tamagawa number conjecture, the strong Stark conjecture and a non-abelian generalization of Rubin's conjecture clue to D. Burns.