Descent on Superelliptic Curves

Details Descent on Superelliptic Curves Descent on Superelliptic Curves

2010-10-12

arxiv.org/abs/1010.2360v4

Mathematics

Number Theory

16 pages, Withdrawn : Undergoing Improvement

Scientific paper

We are concerned with the question of determining the set $C(\Q)$, 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 $\Q$. 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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