Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Théorie d’Iwasawa des représentations $p$-adiques d’un corps local
HTML articles powered by AMS MathViewer

by Frédéric Cherbonnier and Pierre Colmez
J. Amer. Math. Soc. 12 (1999), 241-268


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.
  • Spencer Bloch and Kazuya Kato, $L$-functions and Tamagawa numbers of motives, The Grothendieck Festschrift, Vol. I, Progr. Math., vol. 86, Birkhäuser Boston, Boston, MA, 1990, pp. 333–400. MR 1086888
  • Cherbonnier F.: Représentations $p$-adiques surconvergentes, thèse de l’université d’Orsay, 1996.
  • Cherbonnier F., Colmez P.: Représentations $p$-adiques surconvergentes, Inv. Math. (à paraître).
  • Robert F. Coleman, Division values in local fields, Invent. Math. 53 (1979), no. 2, 91–116. MR 560409, DOI 10.1007/BF01390028
  • Colmez P.: Théorie d’Iwasawa des Représentations de de Rham d’un Corps Local, Ann. of Math. (à paraître).
  • Colmez P.: Représentations cristallines et représentations de hauteur finie, Prépublication du LMENS-97-28, 1997.
  • Jean-Marc Fontaine and Jean-Pierre Wintenberger, Le “corps des normes” de certaines extensions algébriques de corps locaux, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 6, A367–A370 (French, with English summary). MR 526137
  • Jean-Marc Fontaine, Représentations $p$-adiques des corps locaux. I, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 249–309 (French). MR 1106901
  • Jean-Marc Fontaine, Le corps des périodes $p$-adiques, Astérisque 223 (1994), 59–111 (French). With an appendix by Pierre Colmez; Périodes $p$-adiques (Bures-sur-Yvette, 1988). MR 1293971
  • Jean-Marc Fontaine, Représentations $p$-adiques semi-stables, Astérisque 223 (1994), 113–184 (French). With an appendix by Pierre Colmez; Périodes $p$-adiques (Bures-sur-Yvette, 1988). MR 1293972
  • Herr L.: Cohomologie Galoisienne des corps $p$-adiques, thèse de l’université d’Orsay, 1995.
  • Kazuya Kato, Lectures on the approach to Iwasawa theory for Hasse-Weil $L$-functions via $B_\textrm {dR}$. I, Arithmetic algebraic geometry (Trento, 1991) Lecture Notes in Math., vol. 1553, Springer, Berlin, 1993, pp. 50–163. MR 1338860, DOI 10.1007/BFb0084729
  • Bernadette Perrin-Riou, Théorie d’Iwasawa des représentations $p$-adiques sur un corps local, Invent. Math. 115 (1994), no. 1, 81–161 (French). With an appendix by Jean-Marc Fontaine. MR 1248080, DOI 10.1007/BF01231755
  • Jean-Pierre Wintenberger, Le corps des normes de certaines extensions infinies de corps locaux; applications, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 1, 59–89 (French). MR 719763, DOI 10.24033/asens.1440
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 11Sxx
  • Retrieve articles in all journals with MSC (1991): 11Sxx
Bibliographic Information
  • Frédéric Cherbonnier
  • Affiliation: 33 Rue de Poissy, 75005 Paris, France
  • Email:
  • 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
  • MR Author ID: 50720
  • Email:
  • Received by editor(s): November 3, 1997
  • Received by editor(s) in revised form: June 2, 1998
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 241-268
  • MSC (1991): Primary 11Sxx
  • DOI:
  • MathSciNet review: 1626273