Local-global principle for reduced norms over 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.

References in corpus (3)

• Applications of patching to quadratic forms and central simple algebras
• Period-index and u-invariant questions for function fields over complete discretely valued fields
• Refinements to patching and applications to field invariants

Cited by in corpus (3)

• Local-global principles for norm one tori over semi-global fields
• On the Rost divisibility of henselian discrete valuation fields of cohomological dimension 3
• Reduced norms of division algebras over complete discrete valuation fields of local-global type