Let be a totally real abelian number field. By the Kronecker-Weber theorem, there exists an such that . Let be the Galois group of the extension . Let denote the group of units in the ring of integers of , let be the subgroup of consisting of units of the form
Theorem 1 (Thaine).
Suppose is a rational prime not dividing the degree and suppose annihilates the Sylow -subgroup of . Then annihilates the Sylow -subgroup of .
This is one of the most sophisticated results concerning the annihilators of an ideal class group. It is a direct, but more complicated, version of Stickelberger’s theorem, applied to totally real fields (for which Stickelberger’s theorem gives no information).
|Date of creation||2013-03-22 14:12:34|
|Last modified on||2013-03-22 14:12:34|
|Last modified by||mathcam (2727)|