Uniform distribution in subgroups of the Brauer group of an algebraic number field

We construct subgroups of the Brauer group of an algebraic number field whose member classes have Hasse invariants satisfying a rigid arithmetic structure -that of (relative) uniform distribution. After obtaining existence and structure theorems for these subgroups, we focus on the problem of describing algebraic properties satisfied by the central simple algebras in these subgroups. Key results are that splitting fields are determined up to isomorphism, and there exists a distinguished subgroup of central automorphisms which can be extended.