Integral points and Vojta’s conjecture on rational surfaces

Yasufuku, Yu

doi:10.1090/S0002-9947-2011-05320-1

Integral points and Vojta’s conjecture on rational surfaces
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by Yu Yasufuku

Trans. Amer. Math. Soc. 364 (2012), 767-784

DOI: https://doi.org/10.1090/S0002-9947-2011-05320-1

Published electronically: September 15, 2011

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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.

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