  Let T be a complete discrete valuation ring and $\hat{X}$ a smooth projective
curve over $S=\spec(T)$ with closed fibre $X$. Denote by $F$ the function field
of $\hat{X}$ and by $\hat{F}$ the completion of $F$ with respect to the
discrete valuation defined by $X$, the closed fibre. In this paper, we
construct indecomposable and noncrossed product division algebras over $F$.
This is done by defining an index preserving group homomorphism
$s:\br(\hat{F})'\to\br(F)'$, and using it to lift indecomposable and noncrossed
product division algebras over $\hat{F}$.
