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Néron-Tate heights on the Jacobians of high-genus hyperelliptic curves
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Holmes, David, (Researcher in mathematics) (2012) Néron-Tate heights on the Jacobians of high-genus hyperelliptic curves. PhD thesis, University of Warwick.
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WRAP_THESIS_Holmes_2012.pdf - Submitted Version Download (836Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b2682003~S1
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Jacobians, Curves, Elliptic, Integrals, Hyperelliptic | ||||
Official Date: | April 2012 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Siksek, Samir | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Extent: | vi, 118 leaves. | ||||
Language: | eng |
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