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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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Department:
University of Oxford

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Department:
University of Oxford
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Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Language:
English
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