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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Integral points and Vojta’s conjecture on rational surfaces
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by Yu Yasufuku PDF
Trans. Amer. Math. Soc. 364 (2012), 767-784 Request permission

Abstract:

Using an inequality by Corvaja and Zannier about gcd’s of polynomials in $S$-units, we verify Vojta’s conjecture (with respect to integral points) for rational surfaces and triangular divisors. This amounts to a gcd inequality for integral points on $\mathbb {G}_m^2$. The argument in the proof is generalized to give conditions under which Vojta’s conjecture on a variety implies Vojta’s conjecture on its blowup.
References
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Additional Information
  • Yu Yasufuku
  • Affiliation: Department of Mathematics, CUNY-Graduate Center, 365 Fifth Avenue, New York, New York 10016
  • Address at time of publication: Department of Mathematics, Nihon University, 1-8-14 Kanda-Surugadai, Tokyo 101-8308, Japan
  • MR Author ID: 681581
  • Email: yasufuku@post.harvard.edu, yasufuku@math.cst.nihon-u.ac.jp
  • Received by editor(s): June 19, 2009
  • Received by editor(s) in revised form: November 26, 2009, January 26, 2010, and February 13, 2010
  • Published electronically: September 15, 2011
  • Additional Notes: This work was supported in part by NSF VIGRE grant number DMS-9977372
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 767-784
  • MSC (2010): Primary 11J97, 14G40; Secondary 14J26
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05320-1
  • MathSciNet review: 2846352