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Height uniformity for integral points on elliptic curves

Author(s): Su-ion Ih
Journal: Trans. Amer. Math. Soc. 358 (2006), 1657-1675.
MSC (2000): Primary 11G35, 11G50, 14G05
Posted: August 1, 2005
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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.

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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: 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
Posted: August 1, 2005
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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