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arXiv · 1904.00966

Local-global principles for norm one tori over semi-global fields

Sumit Chandra Mishra
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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.

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Sumit Chandra Mishra. 2019-04-01. Local-global principles for norm one tori over semi-global fields. https://doi.org/10.1007/s00209-020-02585-7

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