Counting Rational Points on Ruled Varieties
نویسنده
چکیده
In this paper, we prove a general result computing the number of rational points of bounded height on a projective variety V which is covered by lines. The main technical result used to achieve this is an upper bound on the number of rational points of bounded height on a line. This upper bound is such that it can be easily controlled as the line varies, and hence is used to sum the counting functions of the lines which cover the original variety V . Mathematics Subject Classification: 11G50, 11D45, 11D04, 14G05.
منابع مشابه
Counting rational points on ruled varieties over function fields
Let K be the function field of an algebraic curve C defined over a finite field Fq. Let V ⊂ PK be a projective variety which is a union of lines. We prove a general result computing the number of rational points of bounded height on V/K. We first compute the number of rational points on a general line defined over K, and then sum over the lines covering V . Mathematics Subject Classification: 1...
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تاریخ انتشار 2003