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Thesis

Descent methods and torsion on Jacobians of higher genus curves

Abstract:

In this thesis we accomplish four main results related to Jacobians of curves.

Firstly, we find a large number of hyperelliptic curves of genus 2, 3 and 4 whose Jacobians have torsion points of large order. The genus 2 case is particularly well-studied in the literature, and we provide a new example of a geometrically simple Jacobian of a genus 2 curve with a point of order 25, an order which was not previously known. For geometrically simple Jacobians of curves of genus 3 and 4, we...

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Division:
MPLS
Department:
Mathematical Institute
Department:
University of Oxford
Role:
Author

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Department:
University of Oxford
Role:
Supervisor
Engineering & Physical Sciences Research Council More from this funder
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
Keywords:
Subjects:
UUID:
uuid:04cef70a-2ab9-44c2-8bbe-ca2ac33bfe41
Deposit date:
2019-04-07

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