Every generically trivial torsor under a smooth group scheme over a smooth variety over any field is Zariski semilocally trivial, settling the Grothendieck-Serre question.
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Generically trivial torsors under constant groups
Every generically trivial torsor under a smooth group scheme over a smooth variety over any field is Zariski semilocally trivial, settling the Grothendieck-Serre question.