Local-global principles for torsors over arithmetic curves

@article{Harbater2015LocalglobalPF,
  title={Local-global principles for torsors over arithmetic curves},
  author={D. Harbater and David Julia Daniel Hartmann and David Julia Daniel Krashen},
  journal={American Journal of Mathematics},
  year={2015},
  volume={137},
  pages={1559 - 1612}
}
We consider local-global principles for torsors under linear algebraic groups, over function fields of curves over complete discretely valued fields. The obstruction to such a principle is a version of the Tate-Shafarevich group; and for groups with rational components, we compute it explicitly and show that it is finite. This yields necessary and sufficient conditions for local-global principles to hold. Our results rely on first obtaining a Mayer-Vietoris sequence for Galois cohomology and… Expand
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