By 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.
By Jean-Louis Colliot-Thélène
By Will Sawin
By David Harari
By Pierre Le Boudec
By Cyril Demarche
By Arne Smeets
By Julia Hartmann
By Olivier Wittenberg
By Antoine Chambert-Loir
