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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Théorie d'Iwasawa des représentations $p$-adiques d'un corps local


Authors: Frédéric Cherbonnier and Pierre Colmez
Journal: J. Amer. Math. Soc. 12 (1999), 241-268
MSC (1991): Primary 11Sxx
MathSciNet review: 1626273
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Abstract: This paper takes up the study of Iwasawa theory of $p$-adic representations of a local field via the theory of $(\varphi,\Gamma)$-modules. In particular, a vast generalisation of Coleman's isomorphism is given as well as an explicit reciprocity law relating this isomorphism to Bloch-Kato's exponential maps in the case of a de Rham representation.


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Frédéric Cherbonnier
Affiliation: 33 Rue de Poissy, 75005 Paris, France
Email: frederic.cherbonnier@francetelecom.fr

Pierre Colmez
Affiliation: Département de Mathématiques et Informatique, École Normale Supérieure, U.R.A. 762 du C.N.R.S., 45 rue d’Ulm, 75005 Paris, France; Équipe d’Arithmétique, Institut de Mathématiques, U.M.R. 9994 du C.N.R.S., 4 place Jussieu, 75252 Paris Cedex 05, France
Email: colmez@dmi.ens.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-99-00281-7
PII: S 0894-0347(99)00281-7
Received by editor(s): November 3, 1997
Received by editor(s) in revised form: June 2, 1998
Article copyright: © Copyright 1999 American Mathematical Society