Institut Henri Poincaré

À la redécouverte des points rationnels

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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.