  Since Amitsur's discovery of noncrossed product division algebras more than
35 years ago, their existence over more familiar fields has been an object of
investigation. Brussel's work was a culmination of this effort, exhibiting
noncrossed products over the rational function field k(t) and the Laurent
series field k((t)) over any global field k -- the smallest possible centers of
noncrossed products.
  Witt's theorem gives a transparent description of the Brauer group of k((t))
as the direct sum of the Brauer group of k and the character group of the
absolute Galois group of k. We classify the Brauer classes over k((t))
containing noncrossed products by analyzing the fiber over chi for each
character chi in Witt's theorem. In this way, a picture of the partition of the
Brauer group into crossed products/noncrossed products is obtained, which is in
principle ruled solely by a relation between index and number of roots of
unity. For large indices the noncrossed products occur with a "natural density"
equal to 1.
