  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.

Number Theory