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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF

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?)

  • 1. Allen Altman and Steven Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Mathematics, Vol. 146, Springer-Verlag, Berlin-New York, 1970. MR 0274461 (43 #224)
  • 2. S. Ju. Arakelov, An intersection theory for divisors on an arithmetic surface, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1179–1192 (Russian). MR 0472815 (57 #12505)
  • 3. S. J. Arakelov, Theory of intersections on the arithmetic surface, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 405–408. MR 0466150 (57 #6031)
  • 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 (86e:14009), http://dx.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 (85k:14004)
  • 9. Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725 (80b:14001)
  • 10. Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157 (57 #3116)
  • 11. Ernst Kunz, Kähler differentials, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1986. MR 864975 (88e:14025)
  • 12. Serge Lang, Diophantine geometry, Interscience Tracts in Pure and Applied Mathematics, No. 11, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0142550 (26 #119)
  • 13. Stephen Lichtenbaum, Curves over discrete valuation rings, Amer. J. Math. 90 (1968), 380–405. MR 0230724 (37 #6284)
  • 14. I. R. Shafarevich, Lectures on minimal models and birational transformations of two dimensional schemes, Notes by C. P. Ramanujam. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, No. 37, Tata Institute of Fundamental Research, Bombay, 1966. MR 0217068 (36 #163)
  • 15. Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451 (91k:11049)


Review Information

Reviewer: Joseph H. Silverman
Journal: Bull. Amer. Math. Soc. 21 (1989), 171-176
DOI: http://dx.doi.org/10.1090/S0273-0979-1989-15806-0
PII: S 0273-0979(1989)15806-0