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15 September 2003 Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters
Annette Huber, Guido Kings
Duke Math. J. 119(3): 393-464 (15 September 2003). DOI: 10.1215/S0012-7094-03-11931-6

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.

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Annette Huber. Guido Kings. "Bloch-Kato conjecture and main conjecture of Iwasawa theory for Dirichlet characters." Duke Math. J. 119 (3) 393 - 464, 15 September 2003. https://doi.org/10.1215/S0012-7094-03-11931-6

Information

Published: 15 September 2003
First available in Project Euclid: 23 April 2004

zbMATH: 1044.11095
MathSciNet: MR2002643
Digital Object Identifier: 10.1215/S0012-7094-03-11931-6

Subjects:
Primary: 11G55
Secondary: 11R23, 19F27

Rights: Copyright © 2003 Duke University Press

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Vol.119 • No. 3 • 15 September 2003
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