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Book Review
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Book Information
Author(s):
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:
- 1.
- S. Altman and S. Kleinman, Introduction to Grothendieck duality theory, Lecture Notes in Math., vol. 146, Springer-Verlag, Berlin and New York, 1970. MR 274461
- 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
Additional Information:
Reviewer(s):
Joseph H.
Silverman
Review Information:
Journal:
Bull. Amer. Math. Soc.
21
(1989),
171-176.
DOI:
10.1090/S0273-0979-1989-15806-0
PII:
S 0273-0979(1989)15806-0
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