Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF
Book Information:

Author: Gerd Faltings and Ching-Li Chai
Title: Degeneration of Abelian Varieties
Additional book information: Ergeb. Math. Grenzgeb. (3), vol. 22, Springer-Verlag, New York, 1990, 316 pp., US$39.80. ISBN 3-540-52015-5.

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

  • [1] M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 0268188
  • [2] A. Ash, D. Mumford, M. Rapoport, and Y. Tai, Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Mass., 1975. Lie Groups: History, Frontiers and Applications, Vol. IV. MR 0457437
  • [3] H. Cartan, Fonctions automorphes, Séminaire ENS 1957/58, Benjamin, New York, 1967.
  • [4] Ching-Li Chai, Compactification of Siegel moduli schemes, London Mathematical Society Lecture Note Series, vol. 107, Cambridge University Press, Cambridge, 1985. MR 853543
  • [5] P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 75–109. MR 0262240
  • [6] Groupes de monodromie en géométrie algébrique. I, Lecture Notes in Mathematics, Vol. 288, Springer-Verlag, Berlin-New York, 1972 (French). Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 I); Dirigé par A. Grothendieck. Avec la collaboration de M. Raynaud et D. S. Rim. MR 0354656
  • [7] David Mumford, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 34, Springer-Verlag, Berlin-New York, 1965. MR 0214602
  • [8] D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 0204427
  • [9] David Mumford, Picard groups of moduli problems, Arithmetical Algebraic Geometry (Proc. Conf. Purdue Univ., 1963) Harper & Row, New York, 1965, pp. 33–81. MR 0201443
  • [10] Peter Roquette, Analytic theory of elliptic functions over local fields, Hamburger Mathematische Einzelschriften (N.F.), Heft 1, Vandenhoeck & Ruprecht, Göttingen, 1970. MR 0260753

Review Information:

Reviewer: Michael Raynaud
Journal: Bull. Amer. Math. Soc. 27 (1992), 183-189