Nickel, Andreas (2011) Integrality of Stickelberger elements and the equivariant Tamagawa number conjecture. Preprintreihe der Fakultät Mathematik 29/2011, Working Paper.
Let L/K be a �nite Galois CM-extension of number �elds with Galois group G.
In an earlier paper, the author has de�ned a module SKu(L/K) over the center of
the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian
and, in particular, contains many Stickelberger elements. It was shown that a certain
conjecture on the integrality of SKu(L/K) implies the minus part of the equivariant
Tamagawa number conjecture at an odd prime p for an in�nite class of (non-abelian)
Galois CM-extensions of number �elds which are at most tamely rami�ed above p,
provided that Iwasawa's μ-invariant vanishes. Here, we prove a relevant part of this
integrality conjecture which enables us to deduce the equivariant Tamagawa number
conjecture from the vanishing of μ for the same class of extensions.
|Item Type:||Monograph (Working Paper)|
|Institutions:||Mathematics > Prof. Dr. Guido Kings|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||07 Sep 2011 06:06|
|Last Modified:||07 Sep 2011 06:06|