Rational points on curves with extra structure
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Abstract
The thesis will discuss several techniques used to provably compute the set of rational points on algebraic curves. We apply these together with several tweaks to some curves of arithmetic-geometric significance.
We will consider the problem of provably computing the set of 𝐾-rational points of a curve 𝑋/𝐾, when 𝐾 = Q or some quadratic number field, and often when this curve has some extra structure (e.g. it is a modular curve or a Fermat quartic). While many of the methods used are of Chabauty kind (Chabauty--Coleman, quadratic Chabauty, elliptic curve Chabauty), we will also employ others such as going-up and going-down.
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Attribution 4.0 International