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Bulletin of the American Mathematical Society

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

Book Review

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Book Information:

Author: Serge Lang
Title: Introduction to Arakelov theory
Additional book information: Springer-Verlag, New York, Berlin, Heidelberg, 1988, x + 187 pp., $49.95. ISBN 0-387-96793-1.

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

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  • 2. S. Arakelov, Intersection theory of divisors on an arithmetic surface, Izv. Akad. Nauk 38(1974), 1179-1192. MR 472815
  • 3. S. Arakelov, Theory of intersections of divisors on an arithmetic surface, Proc. Internat. Congr. Math., Vancouver, 1974, pp. 405-408. MR 466150
  • 4. M. Arbarello, M. Cornalba, P. Griffiths, and J. Harris, Geometry of algebraic curves, Springer-Verlag, Berlin and New York, 1985.
  • 5. T. Chinburg, An introduction to Arakelov intersection theory, Arithmetic geometry (Storrs, Conn., 1984) Springer, New York, 1986, pp. 289–307. MR 861981
  • 6. T. Chinburg, Minimal models for curves over Dedekind rings, Arithmetic geometry (Storrs, Conn., 1984) Springer, New York, 1986, pp. 309–326. MR 861982
  • 7. Gerd Faltings, Calculus on arithmetic surfaces, Ann. of Math. (2) 119 (1984), no. 2, 387–424. MR 740897, https://doi.org/10.2307/2007043
  • 8. William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • 9. Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
  • 10. R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin and New York, 1977. MR 463157
  • 11. Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975
  • 12. S. Lang, Fundamentals of diophantine geometry, Springer-Verlag, Berlin and New York, 1983. MR 142550
  • 13. S. Lichtenbaum, Curves over discrete valuation rings, Amer. J. Math. 90(1968), 380-405. MR 230724
  • 14. I. Shafarevich, On minimal models and birational transformations, Tata Institute, Bombay, India, 1966. MR 217068
  • 15. Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451

Review Information:

Reviewer: Joseph H. Silverman
Journal: Bull. Amer. Math. Soc. 21 (1989), 171-176
DOI: https://doi.org/10.1090/S0273-0979-1989-15806-0
American Mathematical Society