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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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?)

[BK]
Bloch, S., Kato, K.: $L$-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift (Vol. I), P. Cartier, et al., eds., Prog. in Math. 86, Boston: Birkhäuser (1990) 333-400. MR 1086888
[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 0510581
[Cn]
Coleman, R.: Division values in local fields, Invent. Math. 53 (1979) 91-116. MR 0560409
[Cz]
Colmez, P.: Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. 148 (1998) 485-571. MR 1668555
[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 1097613
[La]
Lang, S.: Cyclotomic fields I and II, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 1029028
[PR1]
Perrin-Riou, B.: Théorie d'Iwasawa des représentations $p$-adiques sur un corps local, Invent. Math. 115 (1994) 81-149. MR 1248080
[PR2]
-: La fonction $L$ $p$-adique de Kubota-Leopoldt, in: Arithmetic Geometry, Contemp. Math. 174 (1994) 61-93. MR 1299735
[PR3]
-: Fonctions $L$ $p$-adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier 43 (1993) 945-995. MR 1252935
[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 1029028
[Ru2]
-: Euler Systems. Annals of Math. Studies 147, Princeton: Princeton University Press (2000). MR 1749177
[Wi]
Wiles, A.: Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995), 443-551. MR 1333035

Review Information:

Reviewer: Karl Rubin
Affiliation: Stanford University
Email: rubin@math.stanford.edu
Journal: Bull. Amer. Math. Soc. 39 (2002), 557-562
Published electronically: April 15, 2002
Review copyright: © Copyright 2002 American Mathematical Society