Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.582279
Title: Néron-Tate heights on the Jacobians of high-genus hyperelliptic curves
Author: Holmes, David
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2012
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Abstract:
We use Arakelov intersection theory to study heights on the Jacobians of high-genus hyperelliptic curves. The main results in this thesis are: 1) new algorithms for computing Neron-Tate heights of points on hyperelliptic Jacobians of arbitrary dimension, together with worked examples in genera up to 9 (pre-existing methods are restricted to genus at most 2 or 3). 2) a new definition of a naive height of a point on a hyperelliptic Jacobian of arbitrary dimension, which does not make use of a projective embedding of the Jacobian or a quotient thereof. 3) an explicit bound on the difference between the Neron-Tate height and this new naive height. 4) a new algorithm to compute sets of points of Neron-Tate height up to a given bound on a hyperelliptic Jacobian of arbitrary dimension, again without making use of a projective embedding of the Jacobian or a quotient thereof.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.582279  DOI: Not available
Keywords: QA Mathematics
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