  We prove the existence of noncrossed product and indecomposable division
algebras over the function field of a smooth p-adic curve, especially when the
curve does not admit a smooth model over Z_p. Thus we generalize arXiv
0907.0670. To make our constructions, we investigate the lifting of cohomology
classes from the total fraction ring of the closed fiber to the function field
of the curve, over an arbitrary discrete valuation ring of mixed
characteristic.
