 

David Holmes
An Arakelovtheoretic approach to naïve heights on hyperelliptic Jacobians view print


Published: 
October 27, 2014

Keywords: 
NéronTate height, Arakelov theory, heightdifference bounds, hyperelliptic curves 
Subject: 
Primary: 11G30; secondary: 11G50, 37P30 


Abstract
We use Arakelov theory to define a height on divisors of degree zero on a hyperelliptic curve over a global field, and show that this height has computably bounded difference from the NéronTate height of the corresponding point on the Jacobian. We give an algorithm to compute the set of points of bounded height with respect to this new height. This provides an `in principle' solution to the problem of determining the sets of points of bounded NéronTate heights on the Jacobian. We give a worked example of how to compute the bound over a global function field for several curves, of genera up to 11.


Author information
Mathematisch Instituut Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
holmesdst@math.leidenuniv.nl

