Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

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Abstract

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Zp. This is done by defining an index preserving morphism s:Br(K(X))'→Br(K(X))' which splits res:Br(K(X))→Br(K(X))', where K(X) is the completion of K(X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over K(X). © 2010 Elsevier Inc.

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Brussel, E., McKinnie, K., & Tengan, E. (2011). Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves. Advances in Mathematics, 226(5), 4316–4337. https://doi.org/10.1016/j.aim.2010.12.005

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