  Let D be a finite-dimensional central division algebra over a field K. We
define the genus gen(D) of D to be the collection of classes in the Brauer
group of K represented by central division K-algebras D' having the same
maximal subfields as D. In this paper, we describe a general approach to
proving the finiteness of gen(D) and estimating its size that involves the
unramified Brauer group with respect to an appropriate set of discrete
valuations of K.
