An outline of the Flynn-Chabauty method for curves of genus 2 with an application to the curve C : y2 = x5 − 2x

Freiberg, Tristan (Tristan Munro) (2006). An outline of the Flynn-Chabauty method for curves of genus 2 with an application to the curve C : y2 = x5 − 2x MPhil Thesis, School of Physical Sciences, University of Queensland.

       
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Author Freiberg, Tristan (Tristan Munro)
Thesis Title An outline of the Flynn-Chabauty method for curves of genus 2 with an application to the curve C : y2 = x5 − 2x
Formatted title

An outline of the Flynn-Chabauty method for curves of genus 2 with an application to the curve : C : y2 = x5 − 2x 

School, Centre or Institute School of Physical Sciences
Institution University of Queensland
Publication date 2006
Thesis type MPhil Thesis
Supervisor Dr Victor Scharaschkin
Dr Keith Matthews
Total pages 126
Language eng
Subjects L
780101 Mathematical sciences
230102 Number Theory And Field Theory
Formatted abstract

We will outline a method, which we call the Flynn-Chabauty method, for determining the set of rational points on a genus 2 curve, of rank 0 or 1, defined over Q. The method is highly developed, and there is an extensive literature on the subject. Since there is no point in re-writing theorems and proofs that have already been presented superbly, our goals are rather modest. This thesis provides, firstly, a summary of some background theory in the arithmetic of genus 2 curves and their Jacobians. Secondly, it provides a summary of the main concepts and results that are necessary to understand and apply the Flynn-Chabauty method, and an outline of the method itself. Third, we provide some MAPLE code to facilitate the application of the Flynn-Chabauty method to specific curves. Fourth, we apply the Flynn-Chabauty method to the curve C : y2 = x5 − 2x and obtain a complete description of its set of rational points. We hope that this thesis will enable a person with little number-theoretical background to use the Flynn-Chabauty method. We hope that this thesis will also be useful as a guide for the reader who wishes to gain a deeper understanding of the Flynn-Chabauty method.

Keyword Rational points (Geometry)
Additional Notes

Variant title: Flynn-Chabauty method for genus 2 curves

 
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Created: Fri, 21 Nov 2008, 14:34:04 EST