Appears in collection : Rational Points on Fano and Similar Varieties

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.