Non-cyclic class groups and the Brumer–Stark conjecture

Abstract: For an odd prime number p, we consider the p-primary part of the Brumer–Stark conjecture for a cyclic extension of number fields of degree 2p. We extend earlier work of Greither, Roblot, and Tangedal (2004) by proving the conjecture when the minus component of the p-primary part of the class group of K is not a cyclic Galois module. Consequently, we are able to prove the full Brumer–Stark conjecture for some new classes of number field extensions. [Copyright &y& Elsevier]