论文信息 - An explicit theory of heights

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 arbitrary curve of genus 2, and we apply the technique to compute generators of J(Q), the Mordell-Weil group for a selection of rank 1 examples.

E. V. Flynn

[1] D. Mumford. Tata Lectures on Theta I , 1982 .

[2] David Masser,et al. Fields of large transcendence degree generated by values of elliptic functions , 1983 .

[3] E. V. Flynn. Descent via isogeny in dimension 2 , 1994 .

[4] E. V. Flynn. The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field , 1990, Mathematical Proceedings of the Cambridge Philosophical Society.

[5] Computing the Mordell-Weil rank of Jacobians of curves of genus two , 1993 .

[6] G. B. Mathews,et al. Kummer's Quartic Surface , 1990 .

[7] Joseph H. Silverman,et al. The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[8] E. V. Flynn. The group law on the jacobian of a curve of genus 2. , 1993 .

[9] J. Cremona. Algorithms for Modular Elliptic Curves , 1992 .

[10] Edward F. Schaefer. 2-Descent on the Jacobians of Hyperelliptic Curves , 1995 .

[11] The Mordell-Weil Group of Curves of Genus 2 , 1983 .