Base Change for Higher Stickelberger Ideals Original Research Article

To a finite abelian extension of algebraic number fieldsK/kwith Galois groupG, one can attach annth Stickelberger idealI(n) for each non-negative integern. Whenk′ is an intermediate field, we also consider the extensionK/k′, and show that the associatednth Stickelberger idealI′(n) is contained inI(n). Consequently, if a conjecture on the annihilation of the QuillenK-groupK2nof the ring of integersOKbyI(n) holds forK/k, then it also holds forK/k′.