Local-global principles for norm one tori over semi-global fields
Abstract
Let K be a complete discretely valued field with residue field k and F be a function field of a curve over K. Let L/F be a Galois extension of degree n. If n is coprime to char(k), then under some assumptions on k(e.g. k is algebraically closed or a finite field) and on the geometry of the curve, we show that there is a local-global principle with respect to discrete valuations for the norms from the extension L/F.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2019
- DOI:
- 10.48550/arXiv.1904.00966
- arXiv:
- arXiv:1904.00966
- Bibcode:
- 2019arXiv190400966M
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- Mathematische Zeitschrift (2021)