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arXiv · 1010.2360

Descent on superelliptic curves

Michael Mourao
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Abstract

We are concerned with the question of determining the set $C(\mathbb{Q})$, where $C$ is a curve defined by an equation of the form $y^q=f(x)$, where $q$ is an odd prime and $f$ is a polynomial defined over $\mathbb{Q}$. This question can often be answered using a set which encapsulates information about local solubility of a particular collection of covers of $C$. We define this set and show how to compute it.

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Michael Mourao. 2010-10-12. Descent on superelliptic curves. https://arxiv.org/abs/1010.2360

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