|
Remarks about uniform boundedness of rational points over function fields
Author(s):
Lucia
Caporaso
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3475-3484.
MSC (2000):
Primary 14H05, 14H10
Posted:
May 29, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove certain uniform versions of the Mordell Conjecture and of the Shafarevich Conjecture for curves over function fields and their rational points.
References:
-
- [Ab]
- D. Abramovich: Uniformity of stably integral points on elliptic curves, Inventiones Math. 127, 307-317 (1997). MR 98d:14033
- [AV]
- D. Abramovich and J. F. Voloch: Lang's conjectures, fibered powers, and uniformity, New York J. Math. 2, 20-34 (1996) MR 97e:14031
- [Ar]
- S. Ju. Arakelov: Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk. SSSR Ser. Mat. 35, 1269-1293 (1971). MR 48:298
- [BD]
- T. Bandman and G. Dethloff: Estimates of the number of rational mappings from a fixed variety to varieties of general type, Ann. Inst. Fourier (Grenoble) 47 (1997), no. 3, 801-824. MR 98h:14016
- [BM]
- T. Bandman and D. Markushevich: On the number of rational maps between varieties of general type, J. Math. Sci. Univ. Tokyo 1 (1994), no. 2, 423-433. MR 96c:14012
- [B]
- A. Beauville: Exposé No. 6 in Séminaire sur les pinceaux des courbes de genre au moins deux, Astérisque 86 (1981). MR 83c:14020
- [C]
- L. Caporaso: On certain uniformity properties of curves over function fields, Preprint, AG/9906156, Compositio Mathematica 130 (2002), 1-19. MR 2003a:14038
- [CHM]
- L. Caporaso, J. Harris, and B. Mazur: Uniformity of rational points, J. Amer. Math. Soc. 10 (1997), 1-35. MR 97d:14033
- [DF]
- M. De Franchis: Un teorema sulle involuzioni irrazionali, Rend. Circ. Mat. Palermo 36 (1913), 368.
- [HM]
- J. Harris and I. Morrison: Moduli of curves, Graduate Texts in Mathematics 187, Springer-Verlag, New York, 1998. MR 99g:14031
- [HMu]
- J. Harris and D. Mumford: On the Kodaira dimension of the moduli space of curves, Inventiones Math. 67 (1982), 23-88. MR 83i:14018
- [KO]
- S. Kobayashi and T. Ochiai: Meromorphic mappings onto compact complex spaces of general type, Inventiones Math. 31 (1975), 7-16. MR 53:5948
- [Md]
- M. Martin-Deschamps: Conjecture de Shafarevich pour les corps de fonctions sur
 , Astérisque No. 127, Appendice à l'exposé IX (1985), 256-259. - [Ma]
- Y. Manin: Rational points of algebraic curves over function fields, Izv. Akad. Nauk. SSSR Ser. Mat. 27 (1963), 1395-1440. MR 28:1199
- [Mi]
- Y. Miyaoka: Themes and variations on inequalities of Chern classes, Sugaku 41 (1989), 193-207. MR 91j:14003
- [Pa]
- P. Pacelli: Uniform boundedness for rational points, Duke Math. J. 88 (1997), 77-102. MR 98b:14020
- [P]
- A. N. Parshin: Algebraic curves over function fields, Izv. Akad. Nauk. SSSR Ser. Mat. 32 (1968), 1191-1219. MR 41:1740
- [S]
- L. Szpiro: Exposé No. 3 in Séminaire sur les pinceaux des courbes de genre au moins deux, Astérisque 86 (1981). MR 83c:14020
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
14H05, 14H10
Retrieve articles in all Journals with MSC
(2000):
14H05, 14H10
Additional Information:
Lucia
Caporaso
Affiliation:
Department of Mathematics, Università degli Studi Roma III, Largo San Leonardo Murialdo 1, 00146 Rome, Italy
Email:
caporaso@mat.uniroma3.it
DOI:
10.1090/S0002-9947-03-03323-3
PII:
S 0002-9947(03)03323-3
Received by editor(s):
January 10, 2001
Received by editor(s) in revised form:
September 24, 2001
Posted:
May 29, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org