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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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Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Karl Rubin
Title: Euler systems
Additional book information: Ann. of Math. Stud., vol. 147, Princeton Univ. Press, Princeton, NJ, 2000, xii+227 pp., ISBN 0-691-05075-9, $69.50$

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

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Gross, Benedict H. Kolyvagin's work on modular elliptic curves. $L$-functions and arithmetic (Durham, 1989), 235-256, London Math. Soc. Lecture Note Ser., 153, Cambridge Univ. Press, Cambridge, 1991. MR 1110395
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Gross, Benedict H.; Zagier, Don B. Heegner points and derivatives of $L$-series. Invent. Math. 84 (1986), no. 2, 225-320. MR 0833192
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Kolyvagin, V. A. The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 6,1154-1180, 1327 translation in Math. USSR-Izv. 33 (1989), no. 3, 473-499.
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Kolyvagin, V. A. Finiteness of $E(\mathbb{Q})$ and $\underline{III}(E,\mathbb{Q})$ for a subclass of Weil curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), no. 3, 522-540, 670-671; translation in Math. USSR-Izv. 32 (1989), no. 3, 523-541. MR 0954295
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Kolyvagin, V. A. Euler systems. The Grothendieck Festschrift, Vol. II, 435-483, Progr. Math., 87, Birkhäuser Boston, Boston, MA, 1990. MR 1106906
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Kolyvagin, V. A.; Logachev, D. Yu. Finiteness of $\underline{III}$ over totally real fields. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 55 (1991), no. 4, 851-876; translation in Math. USSR-Izv. 39 (1992), no. 1, 829-853. MR 1137589
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Nekovár, Jan. Kolyvagin's method for Chow groups of Kuga-Sato varieties. Invent. Math. 107 (1992), no. 1, 99-125. MR 1135466
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Rubin, Karl. Tate-Shafarevich groups and $L$-functions of elliptic curves with complex multiplication. Invent. Math. 89 (1987), no. 3, 527-559. MR 0903383
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Rubin, Karl. Kolyvagin's system of Gauss sums. Arithmetic algebraic geometry (Texel, 1989), 309-324, Progr. Math., 89, Birkhäuser Boston, Boston, MA, 1991. MR 1085265
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Rubin, Karl. Appendix in Lang, Serge, Cyclotomic fields I and II. Combined second edition, Graduate Texts in Mathematics, 121, Springer-Verlag, New York, 1990. MR 1029028
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Rubin, Karl. The ``main conjectures" of Iwasawa theory for imaginary quadratic fields. Invent. Math. 103 (1991), no. 1, 25-68. MR 1079839
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Scholl, A. J. An introduction to Kato's Euler systems. Galois representations in arithmetic algebraic geometry (Durham, 1996), 379-460, London Math. Soc. Lecture Note Ser., 254, Cambridge Univ. Press, Cambridge, 1998. MR 1696501
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Thaine, Francisco. On the ideal class groups of real abelian number fields. Ann. of Math. (2) 128 (1988), no. 1, 1-18. MR 0951505
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Taylor, Richard; Wiles, Andrew. Ring-theoretic properties of certain Hecke algebras. Ann. of Math. (2) 141 (1995), no. 3, 553-572. MR 1333036
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Wiles, Andrew. Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2) 141 (1995), no. 3, 443-551. MR 1333035
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Zhang, Shouwu. Heights of Heegner cycles and derivatives of $L$-series. Invent. Math. 130 (1997), no. 1, 99-152. MR 1471887
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Zhang, Shouwu. Heights of Heegner points on Shimura curves. Ann. of Math. (2) 153 (2001), no. 1, 27-147.

Review Information:

Reviewer: Henri Darmon
Affiliation: McGill University
Email: darmon@math.mcgill.ca
Journal: Bull. Amer. Math. Soc. 39 (2002), 407-414
Published electronically: April 11, 2002
Review copyright: © Copyright 2002 American Mathematical Society