Manin obstruction
In mathematics, in the field of arithmetic algebraic geometry, the Manin obstruction is attached to a variety X over a global field, which measures the failure of the Hasse principle for X. If the value of the obstruction is non-trivial, then X may have points over all local fields but not over the global field. The Manin obstruction is sometimes called the Brauer–Manin obstruction, as Manin used the Brauer group of X to define it.
For abelian varieties the Manin obstruction is just the Tate–Shafarevich group and fully accounts for the failure of the local-to-global principle. There are however examples, due to Alexei Skorobogatov, of varieties with trivial Manin obstruction which have points everywhere locally and yet no global points.
