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We prove the existence of noncrossed product and indecomposable divisionalgebras over the function field of a smooth p-adic curve, especially when thecurve does not admit a smooth model over Z_p. Thus we generalize arXiv0907.0670. To make our constructions, we investigate the lifting of cohomologyclasses from the total fraction ring of the closed fiber to the function fieldof the curve, over an arbitrary discrete valuation ring of mixedcharacteristic.

Tame Covers and Cohomology of Relative Curves over Complete Discrete Valuation Rings, with Applications to the Brauer Group