The Mathematical Institute, University of Oxford, Eprints Archive

An explicit theory of heights

Flynn, E. V. (1995) An explicit theory of heights. Transactions of the American Mathematical Society, 347 (8). pp. 3003-3015. ISSN 0002-9947

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Jacobians; height constants; generators of the Mordell-Weil group.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:269
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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