A Brumer-Stark Conjecture for non-abelian Galois extensions

Gaëlle Dejou (1) , Xavier-François Roblot (2)

1 ICJ - Institut Camille Jordan
2 CTN - Combinatoire, théorie des nombres

The Brumer-Stark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the Brumer-Stickelberger element constructed from special values of L-functions associated to the extension, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators obtained have special properties. The aim of this article is to propose a generalization of this conjecture to non-abelian Galois extensions that is, in spirit, very similar to the original conjecture.

Domaines: Théorie des nombres [math.NT]

Gaëlle Dejou, Xavier-François Roblot. A Brumer-Stark Conjecture for non-abelian Galois extensions. Journal of Number Theory, 2014, 142, pp.51-88. ⟨10.1016/j.jnt.2014.02.020⟩. ⟨hal-00863162⟩