Formal constructions in the Brauer group of the function field of a 𝑝-adic curve

Abstract

We study the relationship between the cohomology of the function field of a curve over a complete discretely valued field and that of the function ring of curves resulting over its residue field. The results are applied to prove the existence of noncrossed product division algebras and indecomposable division algebras of unequal period and index over the function field of any p p -adic curve, generalizing the results and methods of a previous work of the authors and McKinnie.