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
Full-text PDF Free Access
References | Similar Articles | Additional Information
- D.Abramovich. On the number of stably integral points on an elliptic curve. preprint.
- D.Abramovich. Uniformité des points rationnels des courbes algébriques sur les extensions quadratiques et cubiques. preprint.
- Dan Abramovich and Joe Harris, Abelian varieties and curves in $W_d(C)$, Compositio Math. 78 (1991), no. 2, 227â238. MR 1104789
- S. Ju. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1269â1293 (Russian). MR 0321933
- E. Arbarello, M. Cornalba, P. A. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985. MR 770932
- Edward Bierstone and Pierre D. Milman, A simple constructive proof of canonical resolution of singularities, Effective methods in algebraic geometry (Castiglioncello, 1990) Progr. Math., vol. 94, BirkhĂ€user Boston, Boston, MA, 1991, pp. 11â30. MR 1106412, DOI https://doi.org/10.1007/978-1-4612-0441-1_2
- F. A. Bogomolov, Families of curves on a surface of general type, Dokl. Akad. Nauk SSSR 236 (1977), no. 5, 1041â1044 (Russian). MR 0457450
- 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. 13â31.
- L.Caporaso, J.Harris, B.Mazur. Uniformity of rational points. Preliminary version of this paper, available by anonymous ftp from math.harvard.edu.
- Schémas en groupes. I: Propriétés générales des schémas en groupes, Lecture Notes in Mathematics, Vol. 151, Springer-Verlag, Berlin-New York, 1970 (French). Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3); Dirigé par M. Demazure et A. Grothendieck. MR 0274458
- Lawrence Ein, Subvarieties of generic complete intersections. II, Math. Ann. 289 (1991), no. 3, 465â471. MR 1096182, DOI https://doi.org/10.1007/BF01446583
- RenĂ©e Elkik, SingularitĂ©s rationnelles et dĂ©formations, Invent. Math. 47 (1978), no. 2, 139â147 (French). MR 501926, DOI https://doi.org/10.1007/BF01578068
- Gerd Faltings, The general case of S. Langâs conjecture, Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991) Perspect. Math., vol. 15, Academic Press, San Diego, CA, 1994, pp. 175â182. MR 1307396
- A.Grothendieck. Eléments de Géométrie Algébrique, Chap. 3 Sect. 6.3. (1961).
- Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977
- B.Hassett. Correlation for surfaces of general type. preprint.
- Heisuke Hironaka, Idealistic exponents of singularity, Algebraic geometry (J. J. Sylvester Sympos., Johns Hopkins Univ., Baltimore, Md., 1976) Johns Hopkins Univ. Press, Baltimore, Md., 1977, pp. 52â125. MR 0498562
- JĂĄnos KollĂĄr, Subadditivity of the Kodaira dimension: fibers of general type, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 361â398. MR 946244, DOI https://doi.org/10.2969/aspm/01010361
- JĂĄnos KollĂĄr, Projectivity of complete moduli, J. Differential Geom. 32 (1990), no. 1, 235â268. MR 1064874
- Serge Lang, Hyperbolic and Diophantine analysis, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 159â205. MR 828820, DOI https://doi.org/10.1090/S0273-0979-1986-15426-1
- E.Looijenga. Smooth Deligne-Mumford compactifications by means of Prym levels structires. J.AlgGeom. 3 (1992) p.283-293.
- S.Lu, M. Miyaoka. preprint.
- David Mumford, Stability of projective varieties, Enseign. Math. (2) 23 (1977), no. 1-2, 39â110. MR 450272
- David Mumford and John Fogarty, Geometric invariant theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 34, Springer-Verlag, Berlin, 1982. MR 719371
- Herbert Popp, ModulrĂ€ume algebraischer Mannigfaltigkeiten, Classification of algebraic varieties and compact complex manifolds, Springer, Berlin, 1974, pp. 219â242. Lecture Notes in Math., Vol. 412 (German). MR 0360581
- Herbert Popp, Moduli theory and classification theory of algebraic varieties, Lecture Notes in Mathematics, Vol. 620, Springer-Verlag, Berlin-New York, 1977. MR 0466143
- Miles Reid, Canonical $3$-folds, JournĂ©es de GĂ©ometrie AlgĂ©brique dâAngers, Juillet 1979/Algebraic Geometry, Angers, 1979, Sijthoff & Noordhoff, Alphen aan den RijnâGermantown, Md., 1980, pp. 273â310. MR 605348
- 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.
- 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.
- E.Viehweg. Rational singularities of higher dimensional schemes. Proc. AMS. 63 n.1 (1977) p.6-8.
- Paul Vojta, Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. MR 883451
Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 14G05, 14H10
Retrieve articles in all journals with MSC (1991): 14G05, 14H10
Additional Information
Lucia Caporaso
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford St., Cambridge, Massachusetts 02138
MR Author ID:
345125
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
MR Author ID:
121915
ORCID:
0000-0002-1748-2953
Email:
mazur@zariski.harvard.edu
Received by editor(s):
September 15, 1994
Received by editor(s) in revised form:
March 23, 1995
Article copyright:
© Copyright 1997
American Mathematical Society