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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.04728
- arXiv:
- arXiv:1605.04728
- Bibcode:
- 2016arXiv160504728P
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Rings and Algebras
- E-Print:
- Compositio Math. 154 (2018) 410-458