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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An explicit theory of heights


Author: E. V. Flynn
Journal: Trans. Amer. Math. Soc. 347 (1995), 3003-3015
MSC: Primary 11G10; Secondary 11G30, 14H25, 14K15
MathSciNet review: 1297525
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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 $ \mathcal{J}(\mathbb{Q})$, the Mordell-Weil group for a selection of rank $ 1$ examples.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1297525-9
PII: S 0002-9947(1995)1297525-9
Article copyright: © Copyright 1995 American Mathematical Society