Abstract:

A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words, local norms are global norms. We investigate the norm principle for finite dimensional commutative etale algebras over global fields; since such an algebra is a product of separable extensions, this is often called the multinorm principle. Under the assumption that the etale algebra contains a cyclic factor, we give an explicit description of the Brauer-Manin obstruction to the Hasse principle.  This is a joint work with E. Bayer and R. Parimala.