Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Height uniformity for integral points on elliptic curves


Author: Su-ion Ih
Journal: Trans. Amer. Math. Soc. 358 (2006), 1657-1675
MSC (2000): Primary 11G35, 11G50, 14G05
Published electronically: August 1, 2005
MathSciNet review: 2186991
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We recall the result of D. Abramovich and its generalization by P. Pacelli on the uniformity for stably integral points on elliptic curves. It says that the Lang-Vojta conjecture on the distribution of integral points on a variety of logarithmic general type implies the uniformity for the numbers of stably integral points on elliptic curves. In this paper we will investigate its analogue for their heights under the assumption of the Vojta conjecture. Basically, we will show that the Vojta conjecture gives a naturally expected simple uniformity for their heights.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11G35, 11G50, 14G05

Retrieve articles in all journals with MSC (2000): 11G35, 11G50, 14G05


Additional Information

Su-ion Ih
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602–7403
Address at time of publication: Department of Mathematics, University of Colorado, Campus Box 395, Boulder, Colorado 80309-0395
Email: ih@math.uga.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03760-8
PII: S 0002-9947(05)03760-8
Keywords: Ample divisor, big divisor, canonical divisor, height, height zeta function, symmetric product, variety of general type, Vojta conjecture
Received by editor(s): March 6, 2004
Received by editor(s) in revised form: June 9, 2004
Published electronically: August 1, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.