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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. Chinberg, An introduction to Arakelov intersection theory, Arithmetic Geometry (G. Cornell and J. Silverman, eds. ), Springer-Verlag, Berlin and New York, 1986, pp. 289-308. MR 861981
  • 6. T. Chinberg, Minimal models for curves over Dedekind rings, Arithmetic Geometry (G. Cornell and J. Silverman, eds. ), Springer-Verlag, Berlin and New York, 1986, pp. 309-326. MR 861982
  • 7. G. Faltings, Calculus on arithmetic surfaces, Ann. of Math. (2) 119(1984), 387-424. MR 740897
  • 8. W. Fulton, Intersection theory, Springer-Verlag, Berlin and New York, 1984. MR 732620
  • 9. P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley & Sons, New York, 1978. MR 507725
  • 10. R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin and New York, 1977. MR 463157
  • 11. E. Kunz, Kähler differentials, Vieweg Verlag, 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. P. Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Math., vol. 1239, Springer-Verlag, Berlin and New York, 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