English

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

Number Theory 2019-02-20 v1 Rings and Algebras

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.

Keywords

Cite

@article{arxiv.1605.04728,
  title  = {Local-global principle for reduced norms over function fields of p-adic curves},
  author = {R. Parimala and R. Preeti and V. Suresh},
  journal= {arXiv preprint arXiv:1605.04728},
  year   = {2019}
}