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2021 Greatest common divisors of integral points of numerically equivalent divisors
Julie Tzu-Yueh Wang, Yu Yasufuku
Algebra Number Theory 15(1): 287-305 (2021). DOI: 10.2140/ant.2021.15.287

Abstract

We generalize the gcd results of Corvaja and Zannier and of Levin on 𝔾mn to more general settings. More specifically, we analyze the height of a closed subscheme of codimension at least 2 inside an n-dimensional Cohen–Macaulay projective variety, and show that this height is small when evaluated at integral points with respect to a divisor D when D is a sum of n+1 effective divisors which are all numerically equivalent to some multiples of a fixed ample divisor. Our method is inspired by Silverman’s gcd estimate, but instead of his usage of Vojta’s conjecture, we use the recent result of Ru and Vojta.

Citation

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Julie Tzu-Yueh Wang. Yu Yasufuku. "Greatest common divisors of integral points of numerically equivalent divisors." Algebra Number Theory 15 (1) 287 - 305, 2021. https://doi.org/10.2140/ant.2021.15.287

Information

Received: 25 February 2020; Revised: 2 May 2020; Accepted: 2 July 2020; Published: 2021
First available in Project Euclid: 17 March 2021

Digital Object Identifier: 10.2140/ant.2021.15.287

Subjects:
Primary: 11J97
Secondary: 11J87 , 14G05 , 32A22

Keywords: blowups , entire curves , greatest common divisors , height inequality , Integral points , Schmidt subspace theorem , Vojta's conjecture

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.15 • No. 1 • 2021
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