The local-global principle for stacky curves
Bjorn Poonen
For smooth projective curves of genus \(g\) over a number field,
the local-global principle holds when \(g=0\) and can fail for \(g=1\),
as has been known since the 1940s. Stacky curves, however,
can have fractional genus. We construct stacky curves of genus \(1/2\)
that violate the local-global principle, and show that \(1/2\) cannot
be reduced. This is joint work with Manjul Bhargava.