Computing the rational torsion subgroup of Jacobians of hyperelliptic curves.

Reitsma, Berno (2020) Computing the rational torsion subgroup of Jacobians of hyperelliptic curves. Master's Thesis / Essay, Mathematics.

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Abstract

This thesis describes and proves the correctness of an algorithm that computes the rational torsion subgroup for the Jacobian of any hyperelliptic curve, and describes the explicit theory that is required by this algorithm. It does not require a procedure that performs the group law on the rational points of the Jacobian. Furthermore, all the required procedures are explicitly described and implemented for Jacobians of hyperelliptic curves of genus 3. Both the design of the algorithm and many required procedures are based on work by Michael Stoll. The rational torsion structures of many Jacobians of hyperelliptic curves of genus 3 with low discriminant have been computed for the LMFDB.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Muller, J.S. and Top, J.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	30 Nov 2020 14:12
Last Modified:	30 Nov 2020 14:12
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/23649

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