Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(e) ISSN 0894-0347(p)

     

Uniformity of rational points

Author(s): Lucia Caporaso; Joe Harris; Barry Mazur
Journal: J. Amer. Math. Soc. 10 (1997), 1-35.
MSC (1991): Primary 14G05, 14H10
MathSciNet review: 1325796
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[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


Similar Articles:

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
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: 10.1090/S0894-0347-97-00195-1
PII: S 0894-0347(97)00195-1
Received by editor(s): September 15, 1994
Received by editor(s) in revised form: March 23, 1995
Copyright of article: Copyright 1997, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia