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On the Units of Coordinate Rings of Algebraic Curves

Koster, C. J. (2014) On the Units of Coordinate Rings of Algebraic Curves. Master's Thesis / Essay, Mathematics.

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Abstract

In this thesis we have investigated the problem of finding the unit group of the coordinate ring of algebraic curves, and in particular of hyperelliptic curves. The existence of nontrivial units is linked to linear combinations of the points at infinity being torsion in the Jacobian of the curve. We have characterized the form of the unit group for hyperelliptic curves and have given many properties of it. Different methods were used to find examples of genus-2 hyperelliptic curves over $qq$ with nontrivial unit group. Finally, we briefly looked at the situation for curves of genus larger than 2.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 07:58
Last Modified: 15 Feb 2018 07:58
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/12114

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