Local-global principle for reduced norms over function fields of p-adic curves

R. Parimala, R. Preeti, V. Suresh

Published 2016-05-16Version 1

Let F be a function field in one variable over a p-adic field and D a central division algebra over F of degree n coprime to p. We prove that Suslin invariant detects whether an element in F is a reduced norm. This leads to a local-global principle for reduced norms with respect to all discrete valuations of F.