| Let T be a complete discrete valuation ring with uniformizer t, and Xˆ a smooth projective curve over S = SpecT. Let F = K( Xˆ) be the function field and let Fˆ = Kˆ(Xˆ) be the completion of F with respect to the discrete valuation defined by the closed fibre X.;In this paper, we construct indecomposable and noncrossed product division algebras over F. This is done by defining an index-preserving homomorphism and using this map s to lift indecomposable and noncrossed product division algebras over Fˆ to indecomposable and noncrossed product division algebras over F, respectively. |
