Nickel, Andreas (2011) On the equivariant Tamagawa number conjecture in tame CM-extensions. MATHEMATISCHE ZEITSCHRIFT, 268 (1-2). pp. 1-35. ISSN 0025-5874,
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Let L/K be a finite Galois CM-extension with Galois group G. The Equivariant Tamagawa Number Conjecture (ETNC) for the pair (h(0)(Spec(L))(0), ZG) naturally decomposes into p-parts, where p runs over all rational primes. If p is odd, these p-parts in turn decompose into a plus and a minus part. Let L/K be tame above p. We show that a certain ray class group of L defines an element in K-0(Z(p)G-, Q(p)) which is determined by a corresponding Stickelberger element if and only if the minus part of the ETNC at p holds. For this we use the Lifted Root Number Conjecture for small sets of places which is equivalent to the ETNC in the number field case. For abelian G, we show that the minus part of the ETNC at p implies the Strong Brumer-Stark Conjecture at p. We prove the minus part of the ETNC at p for almost all primes p.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TOTALLY-REAL FIELDS; FITTING IDEALS; IWASAWA THEORY; UNITS; COHOMOLOGY; VALUES; S=0; Equivariant L-values; Tamagawa numbers; Strong Brumer-Stark Conjecture; CM-extensions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 15 Jun 2020 14:06 |
| Last Modified: | 15 Jun 2020 14:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20784 |
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