Mathematics – Number Theory
Scientific paper
2009-08-15
Mathematics
Number Theory
52 pages
Scientific paper
We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localisation by using Oliver-Taylor's theory upon integral logarithms. This calculation reduces the existence of the non-commutative p-adic zeta function to certain congruence conditions among abelian p-adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne-Ribet's theory and certain inductive technique. As an application we shall prove a special case of (the p-part of) the non-commutative equivariant Tamagawa number conjecture for critical Tate motives. The main results of this paper give generalisation of those of the preceding paper of the author.
No associations
LandOfFree
Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-76134