The Brumer-Stark Conjecture in Some Families of Extensions of Specified Degree

Cornelius Greither (1) , Xavier-François Roblot (2) , Brett Tangedal (3)

1 Institute for Theoretical Computer Science and Mathematics
2 IGD - Institut Girard Desargues
3 Department of Mathematics and Statistics

As a starting point, an important link is established between Brumer's conjecture and the Brumer-Stark conjecture which allows one to translate recent progress on the former into new results on the latter. For example, if K/F is an abelian extension of relative degree 2p, p an odd prime, we prove the ℓ-part of the Brumer-Stark conjecture for all odd primes ℓ≠p with F belonging to a wide class of base fields. In the same setting, we study the 2-part and p-part of Brumer-Stark with no special restriction on F and are left with only two well-defined specific classes of extensions that elude proof. Extensive computations were carried out within these two classes and a complete numerical proof of the Brumer-Stark conjecture was obtained in all cases.

Domaines: Théorie des nombres [math.NT]

Cornelius Greither, Xavier-François Roblot, Brett Tangedal. The Brumer-Stark Conjecture in Some Families of Extensions of Specified Degree. Mathematics of Computation, 2004, 73 (245), pp.297-315. ⟨hal-00863128⟩