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# 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.