*"Curves dominated by an unramified cover of another
curve"*

Bjorn Poonen, University of California, Berkeley

**Abstract:**

Let X be a curve of genus at least 2 over a number field F. If Y is an
unramified cover of X, the Chevalley-Weil descent method reduces the problem of
determining X(F) to the problem of determining Y(F') for some finite extension
F' of F. Also, if X dominates Y, where Y also has genus at least 2, then the
problem of determining X(F) can trivially be reduced to the problem of
determining Y(F). We survey what is known about the transitive relation (not an
equivalence relation) on curves induced by these two relationships.