Brauer–Manin obstruction to the local–global principle for the embedding problem.

We study an analogue of the Brauer–Manin obstruction to the local–global principle for embedding problems over global fields. We will prove the analogues of several fundamental structural results. In particular we show that the (algebraic) Brauer–Manin obstruction is the only one to strong approximation when the embedding problem has abelian kernel. [ABSTRACT FROM AUTHOR]