Local-global principles for torsors over arithmetic curves

Details Local-global principles for torsors over arithmetic curves Local-global principles for torsors over arithmetic curves

2011-08-16

arxiv.org/abs/1108.3323v2

Mathematics

Number Theory

46 pages; some rewording, additional comments and references

Scientific paper

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 we show that it is finite in important cases. Moreover we obtain necessary and sufficient conditions for local-global principles to hold. The proofs use techniques from patching. We also give new applications to quadratic forms and central simple algebras.

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