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Book Review

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Book Information:

Author: Bernadette Perrin-Riou
Title: $p$-Adic $L$-functions and $p$-adic representations
Additional book information: translated by Leila Schneps, Amer. Math. Soc., Providence, RI, 2000, xx + 150 pp., ISBN 0-8218-1946-1, $49.00

References [Enhancements On Off] (What's this?)

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  • [BCDT] Breuil, C., Conrad, B., Diamond, F., Taylor, R.: On the modularity of elliptic curves over ${\mathbf Q}$: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), 843-939.
  • [CW] Coates, J., Wiles, A.: On $p$-adic $L$-functions and elliptic units, J. Austral. Math. Soc. (ser. A) 26 (1978) 1-25. MR 80a:12007
  • [Cn] Coleman, R.: Division values in local fields, Invent. Math. 53 (1979) 91-116. MR 81g:12017
  • [Cz] Colmez, P.: Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. 148 (1998) 485-571. MR 2000f:11077
  • [Gr] Greenberg, R.: Iwasawa theory for $p$-adic representations, in: Algebraic number theory in honor of K. Iwasawa, J. Coates et al., eds., Adv. Stud. in Pure Math. 17, Boston: Academic Press (1989) 97-137. MR 92c:11116
  • [La] Lang, S.: Cyclotomic fields I and II, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 91c:11001
  • [PR1] Perrin-Riou, B.: Théorie d'Iwasawa des représentations $p$-adiques sur un corps local, Invent. Math. 115 (1994) 81-149. MR 95c:11082
  • [PR2] -: La fonction $L$ $p$-adique de Kubota-Leopoldt, in: Arithmetic Geometry, Contemp. Math. 174 (1994) 61-93. MR 96b:11087
  • [PR3] -: Fonctions $L$ $p$-adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier 43 (1993) 945-995. MR 95d:11081
  • [Ru1] Rubin, K.: The main conjecture. Appendix to: Cyclotomic fields I and II, S. Lang, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 91c:11001
  • [Ru2] -: Euler Systems. Annals of Math. Studies 147, Princeton: Princeton University Press (2000). MR 2001g:11170
  • [Wi] Wiles, A.: Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995), 443-551. MR 96d:11071

Review Information:

Reviewer: Karl Rubin
Affiliation: Stanford University
Email: rubin@math.stanford.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 557-562
MSC (2000): Primary 11R23; Secondary 11F80, 11G40, 11R34, 11S25
Published electronically: April 15, 2002
Review copyright: © Copyright 2002 American Mathematical Society
American Mathematical Society