On non-abelian Stark-type conjectures

Nickel, Andreas

Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2577-2608.

Nous présentons des généralisations non abéliennes de la conjecture de Brumer, de la conjecture de Brumer-Stark et de la propriété forte de Brumer-Stark, qui sont associées à une CM-extension galoisienne de corps de nombres. De plus, nous étudions les liens avec la conjecture équivariante sur les nombres de Tamagawa, la conjecture forte de Stark et la généralisation non abélienne d’une conjecture de Rubin due à D. Burns.

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 due to D. Burns.

Classification : 11R42, 11R29
Keywords: Stark conjectures, $L$-values, class groups
Mot clés : conjectures de Stark, valeurs des fonctions $L$, groupes de classe

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