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Mathematics of Computation

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Computing canonical heights using arithmetic intersection theory

Author: Jan Steffen Müller
Journal: Math. Comp. 83 (2014), 311-336
MSC (2010): Primary 11G50; Secondary 11G10, 11G30, 14G40
Published electronically: June 14, 2013
MathSciNet review: 3120591
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Abstract: For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height of a point on the Jacobian of a smooth projective curve can be computed using arithmetic intersection theory on a regular model of the curve in practice. In the case of hyperelliptic curves we present a complete algorithm that has been implemented in Magma. Several examples are computed and the behavior of the running time is discussed.

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Additional Information

Jan Steffen Müller
Affiliation: Fachbereich Mathematik, Universität Hamburg

Received by editor(s): June 29, 2011
Received by editor(s) in revised form: January 27, 2012, and March 5, 2012
Published electronically: June 14, 2013
Additional Notes: This work was supported by DFG-grant STO 299/5-1
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.