Nickel, Andreas (2011) On the equivariant Tamagawa number conjecture in tame CM-extensions, II. COMPOSITIO MATHEMATICA, 147 (4). pp. 1179-1204. ISSN 0010-437X,
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We use the notion of non-commutative Fitting invariants to give a reformulation of the equivariant Iwasawa main conjecture (EIMC) attached to an extension F/K of totally real fields with Galois group g, where K is a global number field and g is a p-adic Lie group of dimension one for an odd prime p. We attach to each finite Galois CM-extension L/K with Galois group G a module SKu(L/K) over the center of the group ring ZG which coincides with the Sinnott-Kurihara ideal if G is abelian. We state a conjecture on the integrality of SKu(L/K) which follows from the equivariant Tamagawa number conjecture (ETNC) in many cases, and is a theorem for abelian G. Assuming the vanishing of the Iwasawa it-invariant, we compute Fitting invariants of certain Iwasawa modules via the EIMC, and we show that this implies the minus part of the ETNC at p for an infinite class of (non-abelian) Galois CM-extensions of number fields which are at most tamely ramified above p, provided that (an appropriate p-part of) the integrality conjecture holds.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | TOTALLY-REAL FIELDS; IWASAWA THEORY; FITTING IDEALS; INTEGERS; VALUES; UNITS; Tamagawa number; equivariant L-values; Iwasawa main conjecture |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Jun 2020 07:06 |
| Last Modified: | 08 Jun 2020 07:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20571 |
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