Vol. 15, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Greatest common divisors of integral points of numerically equivalent divisors

Julie Tzu-Yueh Wang and Yu Yasufuku

Vol. 15 (2021), No. 1, 287–305
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.

Keywords
height inequality, integral points, greatest common divisors, blowups, Schmidt subspace theorem, Vojta's conjecture, entire curves
Mathematical Subject Classification 2010
Primary: 11J97
Secondary: 11J87, 14G05, 32A22
Milestones
Received: 25 February 2020
Revised: 2 May 2020
Accepted: 2 July 2020
Published: 1 March 2021
Authors
Julie Tzu-Yueh Wang
Institute of Mathematics
Academia Sinica
Taipei
Taiwan
Yu Yasufuku
Department of Mathematics, College of Science and Technology
Nihon University
Chiyoda-ku, Tokyo
Japan