منابع مشابه
An Explicit Theory of Heights
We consider the problem of explicitly determining the naive height constants for Jacobians of hyperelliptic curves. For genus > 1, it is impractical to apply Hilbert’s Nullstellensatz directly to the defining equations of the duplication law; we indicate how this technical difficulty can be overcome by use of isogenies. The height constants are computed in detail for the Jacobian of an arbitrar...
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The goal of this paper is to take up the approaches used to deal with Jacobians and Kummer surfaces of curves of genus 2 by Cassels and Flynn [CF] and by the author [Sto1, Sto3] and extend them to hyperelliptic curves of genus 3. Such a curve C is given by an equation of the form y = f(x), where f is a squarefree polynomial of degree 7 or 8. We denote its Jacobian by J . Identifying points with...
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— By using the slope method, we obtain an explicit uniform estimation for the density of rational points in an arithmetic projective variety with given degree and dimension, embedded in a given arithmetic projective space. Résumé. — On obtient, en utilisant la méthode de pentes, une estimation uniforme et explicite de la densité des points rationnels dans une variété arithmétique projective de ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1995
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1995-1297525-9