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

TL;DR

This paper establishes a local-global principle for reduced norms over function fields of p-adic curves, showing that Suslin invariant effectively detects reduced norms in this setting.

Contribution

It proves that Suslin invariant can determine reduced norms over function fields of p-adic curves, leading to a new local-global principle for these norms.

Findings

Suslin invariant detects reduced norms over F

Established a local-global principle for reduced norms

Applied to function fields of p-adic curves

Abstract

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.