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Uniformity of rational points


Authors: Lucia Caporaso, Joe Harris and Barry Mazur
Journal: J. Amer. Math. Soc. 10 (1997), 1-35
MSC (1991): Primary 14G05, 14H10
DOI: https://doi.org/10.1090/S0894-0347-97-00195-1
MathSciNet review: 1325796
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  • [Ab1] D.Abramovich. On the number of stably integral points on an elliptic curve. preprint.
  • [Ab2] D.Abramovich. Uniformité des points rationnels des courbes algébriques sur les extensions quadratiques et cubiques. preprint.
  • [AH] D.Abramovich, J.Harris. Abelian varieties and curves in $W_d(C)$. Compositio Math. 78 (1991) p. 227-238. MR 92c:14022
  • [Ar] S.Ju.Arakelov. Families of algebraic curves with fixed degeneracies. Izv. Akad. Nauk. SSSR, Ser. Math 35 (1971); English translation Math USSR Izv. 5 (1971) p. 1277-1302. MR 48:298
  • [ACGH] E.Arbarello, M.Cornalba, P.Griffiths, J.Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, NY. MR 86h:14019
  • [BM] E. Bierstone, P. Milman. A simple constructive proof of canonical resolution of singularities. In: Effective Methods in Algebraic Geometry, Progress in Math. vol. 94, Birkhauser Boston 1991, p. 11-30. MR 92h:32053
  • [B] F.Bogomolov. Families of curves on surfaces of general type. Dokl. AN SSSR 236 (6) (1977) p. 1294-1297 (English: Sov. Math. Doklady 1041-1044). MR 56:15655
  • [CHM] L.Caporaso, J.Harris, B.Mazur. How many rational points can a curve have? Proceedings of the Texel Conference, Progress in Math. vol. 129, Birkhauser Boston, 1995, p. 13-31. CMP 96:04
  • [CHM1] L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. Preliminary version of this paper, available by anonymous ftp from math.harvard.edu.
  • [SGA] M.Demazure Exposé IV: Topologies et Faisceaux 6.5, 6.5. In: SGA 3 (Schemas en Groupes I), Springer Lecture Notes in Mathematics 151 (1970) MR 43:223a
  • [E] L.Ein. Subvarieties of generic complete intersections, II. Math. Ann. (289), pp 465-471. MR 92h:14002
  • [El] R.Elkik, Singularités rationnelles et deformations., Invent. Math. 47, (1978) p. 139-147. MR 80c:14004
  • [F] G.Faltings. The general case of S. Lang's Conjecture. Barsotti Symposium in Algebraic Geometry, Perspectives in Mathematics, Academic Press, Inc. 1994 p.175-182. MR 95m:11061
  • [EGA] A.Grothendieck. Eléments de Géométrie Algébrique, Chap. 3 Sect. 6.3. (1961). MR 29:1209
  • [H] R.Hartshorne. Ample subvarieties of algebraic varieties. Lecture Notes in Math. 156. Springer Verlag (1970). MR 44:211
  • [Ha] B.Hassett. Correlation for surfaces of general type. preprint.
  • [Hi] H. Hironaka. Idealistic exponents of singularity. In: Algebraic Geometry, J.J.Sylvester Symposium, Johns Hopkins Univ., Baltimore, Md., 1976, Johns Hopkins Univ. Press, Baltimore, Md., 1977, p. 52-125. MR 58:16661
  • [Ko] J.Kollár. Subadditivity of the Kodaira dimension: fibers of general type. Adv. Stud. in Pure Math. 10 (1987) p. 361-398. MR 89i:14029
  • [Ko1] J.Kollár. Projectivity of complete moduli. J. Diff. Geom 32 (1990) 235-268. MR 92e:14008
  • [L] S.Lang. Hyperbolic and diophantine analysis. Bull. Amer. Math. Soc. 14 , No. 2 (1986) p. 159-205. MR 87h:32051
  • [Lo] E.Looijenga. Smooth Deligne-Mumford compactifications by means of Prym levels structires. J.AlgGeom. 3 (1992) p.283-293.
  • [LM] S.Lu, M. Miyaoka. preprint.
  • [Mu] D.Mumford. Stability of projective varieties. L'Enseignement Mathématique 23 (1977) p. 39-110. MR 56:8568
  • [GIT] D.Mumford, J.Fogarty. Geometric Invariant Theory. Springer Verlag (1982). MR 86a:14006
  • [Po1] H.Popp. Modulräume algebraischer Mannigfaltigkeiten. Classification of Algebraic Varieties and Compact Complex Manifolds, Springer Lecture Notes 412, 1974. MR 50:13029
  • [Po2] H.Popp. Moduli Theory and Classification Theory of Algebraic Varieties. Springer Lecture Notes 620, 1977. MR 57:6024
  • [R] M.Reid. Canonical threefolds. Géométrie Algébrique, Angers 1979 Sijthoff and Nordhoff (1980) p. 273-310. MR 82i:14025
  • [V] E.Viehweg. Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces. Adv. Stud. in Pure Math. 1 (1983) p. 329-353.
  • [V1] E.Viehweg. Canonical divisors and the additivity of the Kodaira dimension for morphisms of relative dimension one. Compositio Math. 35, Fasc 2 (1977) p. 197-223.
  • [V2] E.Viehweg. Rational singularities of higher dimensional schemes. Proc. AMS. 63 n.1 (1977) p.6-8.
  • [Vo] P.Vojta Diophantine Approximations and Value Distribution Theory. Springer Lecture Notes in Mathematics 1239 (1987) MR 91k:11049

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Additional Information

Lucia Caporaso
Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
Email: caporaso@zariski.harvard.edu

Joe Harris
Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
Email: harris@zariski.harvard.edu

Barry Mazur
Affiliation: Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
Email: mazur@zariski.harvard.edu

DOI: https://doi.org/10.1090/S0894-0347-97-00195-1
Received by editor(s): September 15, 1994
Received by editor(s) in revised form: March 23, 1995
Article copyright: © Copyright 1997 American Mathematical Society

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