Manin obstruction

In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction (named after Yuri Manin) is attached to a variety X over a global field, which measures the failure of the Hasse principle for X.

For abelian varieties the Manin obstruction is just the Tate–Shafarevich group and fully accounts for the failure of the local-to-global principle (under the assumption that the Tate–Shafarevich group is finite).

There are however examples, due to Alexei Skorobogatov, of varieties with trivial Manin obstruction which have points everywhere locally and yet no global points.

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