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Uniform bounds for stably integral points on elliptic curves

Author(s): Patricia L. Pacelli
Journal: Proc. Amer. Math. Soc. 127 (1999), 2535-2546.
MSC (1991): Primary 11Gxx, 14Gxx
Posted: May 19, 1999
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Abstract: We show that a conjecture by Lang and Vojta regarding integral points on varieties of logarithmic general type implies the existence of a uniform bound on the number of stably $S$-integral points on an elliptic curve over a degree-$d$ number field.

References:

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D. Abramovich. Uniformity of stably integral points on elliptic curves, Invent. Math. 127 (1997), p. 307-317. MR 98d:14033

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S. Lang. Hyperbolic diophantine analysis, Bull. A.M.S. 14 (1986), p. 159-205. MR 87h:32051

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P. Pacelli. Uniform boundedness for rational points, Duke Math. J. vol. 88 no. 1 (1997), p. 77-102. MR 98b:14020

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K. Rubin and A. Silverberg. Families of elliptic curves with constant mod $p$ representations, Elliptic curves, modular forms, and Fermat's last theorem (Hong Kong, 1993), Ser. Number Theory, I, Internat. Press, Cambridge, MA. (1995), p. 148-161. MR 96j:11078

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Additional Information:

Patricia L. Pacelli
Affiliation: Department of Mathematics, Barnard College, Columbia University, New York, New York 10027-6598
Email: pacelli@math.columbia.edu

DOI: 10.1090/S0002-9939-99-05429-5
PII: S 0002-9939(99)05429-5
Received by editor(s): September 2, 1997
Posted: May 19, 1999
Additional Notes: It is a pleasure to thank Dan Abramovich and Glenn Stevens for encouraging me to pursue this work. Dan Abramovich was also kind enough to read earlier versions of this paper and provide extremely helpful comments
Communicated by: Ron Donagi
Copyright of article: Copyright 1999, American Mathematical Society

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