Vojta's Inequality and Rational and Integral Points of Bounded Degree on Curves

2006/01/27 by Aaron Levin, Levin, Aaron
Mathematics · #11G30 (Primary) 14G40 #14H25 (secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G30 #msc:14G40 #msc:14H25

paper · pdf · doi:10.48550/arxiv.math/0601686

11 pages

arxiv created 2006/01/27 · arxiv updated 2009/12/01

Abstract

Let C in C₁xC₂ be a curve of type (d₁,d₂) in the product of the two curves C₁ and C₂. Let d be a positive integer. We prove that if a certain inequality involving d₁, d₂, d, and the genera of the curves C₁, C₂, and C is satisfied, then the set of points P in C(\kbar) with [k(P):k]<=d is finite for any number field k. We prove a similar result for integral points of bounded degree on C. These results are obtained as consequences of an inequality of Vojta which generalizes the Roth-Wirsing theorem to curves.

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