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

TL;DR

This paper constructs specific complex division algebras over function fields of p-adic curves by developing a morphism that lifts properties from completions to the original fields, advancing algebraic understanding.

Contribution

It introduces an index-preserving morphism that enables lifting indecomposable and noncrossed product division algebras from completions to original function fields.

Findings

Constructed indecomposable division algebras over function fields.

Developed a morphism that splits the restriction map in Brauer groups.

Enabled lifting of algebra properties from completions to original fields.

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(\hat K(X))' -> Br(K(X))' which splits res:Br(K(X)) -> Br(\hat K(X)), where \hat K(X) is the completion of K(X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over \hat K(X).