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