Counting rational points on ruled varieties over function fields
نویسنده
چکیده
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: 11D04 (11G35, 11G50, 11D45, 14G05, 14G25)
منابع مشابه
Counting Rational Points on Ruled Varieties
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 fu...
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