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

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

2006-01-27

arxiv.org/abs/math/0601686v1

Mathematics

Number Theory

11 pages

Scientific paper

Let C in C_1xC_2 be a curve of type (d_1,d_2) in the product of the two curves C_1 and C_2. Let d be a positive integer. We prove that if a certain inequality involving d_1, d_2, d, and the genera of the curves C_1, C_2, 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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