Huber, A. and Kings, Guido (2003) Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters. DUKE MATHEMATICAL JOURNAL, 119 (3). pp. 393-464. ISSN 0012-7094, 1547-7398
Full text not available from this repository. (Request a copy)Abstract
The Tamagawa number conjecture proposed by S. Bloch and K Kato describes the "special values" of L functions in terms of cohomological data. The main conjecture of Iwasawa theory describes a p-adic L-function in terms of the structure of modules for the Iwasawa algebra. We give a complete proof of both conjectures (up to the prime 2) for L functions attached to Dirichlet characters. We use the insight of Kato and B. Perrin-Riou that these two conjectures can be seen as incarnations of the same mathematical content. In particular, they imply each other. By a bootstrapping process using the theory of Euler systems and explicit reciprocity laws, both conjectures are reduced to the analytic class number formula. Technical problems with primes dividing the order of the character are avoided by using the correct cohomological formulation of the main conjecture.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ETALE K-THEORY; MOTIVES; FORMULAS; FIELD; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Guido Kings |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Jul 2021 11:15 |
| Last Modified: | 28 Jul 2021 11:15 |
| URI: | https://pred.uni-regensburg.de/id/eprint/38605 |
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