|Title: Local-global principles for norm one tori over semi-global fields.|
|Speaker: Sumit Chandra Mishra of Emory University|
|Contact: David Zureick-Brown, DAVID.M.BROWN.JR@GMAIL.COM|
|Date: 2020-03-24 at 4:00PM|
Let K be a complete discretely valued field with residue field k (e.g. k((t)) ). Let n be an integer coprime to char(k). Let F = K(x) be the rational function field in one variable over F and L/F be any Galois extension of degree n. Suppose that either k is algebraically closed or k is finite field containing a primitive nth root of unity. Then we show that an element in F? is a norm from the extension L/F if and only if it is a norm from the corresponding extensions over the completions of F at all discrete valuations of F. We also prove that such a local-global principle holds for product of norms from cyclic extensions of prime degree if k is algebraically closed.
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