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Let T be a complete discrete valuation ring and $\hat{X}$ a smooth projectivecurve over $S=\spec(T)$ with closed fibre $X$. Denote by $F$ the function fieldof $\hat{X}$ and by $\hat{F}$ the completion of $F$ with respect to thediscrete valuation defined by $X$, the closed fibre. In this paper, weconstruct 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 noncrossedproduct division algebras over $\hat{F}$.

Indecomposable and Noncrossed Product Division Algebras over Curves over Complete Discrete Valuation Rings