We generalize the gcd results of Corvaja and Zannier and of Levin on to more general settings. More specifically, we analyze the height of a closed subscheme of codimension at least inside an -dimensional Cohen–Macaulay projective variety, and show that this height is small when evaluated at integral points with respect to a divisor when is a sum of 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.
"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