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

2009/07/03 by Eric Brussel, Brussel, Eric, Kelly McKinnie +3
Mathematics · #16K20 #16K50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA #msc:16K20 #msc:16K50

paper · pdf · doi:10.48550/arxiv.0907.0670

22 pages

arxiv created 2010/11/23 · arxiv updated 2010/11/24

Abstract

We construct indecomposable and noncrossed product division algebras over function fields of smooth curves X over Z_p. 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).

Related

• Indecomposable and Noncrossed Product Division Algebras over Curves over Complete Discrete Valuation Rings
• Cyclic Algebras over p-adic curves
• Tame Covers and Cohomology of Relative Curves over Complete Discrete Valuation Rings, with Applications to the Brauer Group
• Division Algebra Cyclicity in Prime Degree over a p-Adic Curve
• Tame division algebras of prime period over function fields of p-adic curves