# MATH Seminar

Title: Local-global principles for norm one tori over semi-global fields.
Defense: Dissertation
Speaker: Sumit Chandra Mishra of Emory University
Contact: David Zureick-Brown, DAVID.M.BROWN.JR@GMAIL.COM
Date: 2020-03-24 at 4:00PM
Venue: https://emory.zoom.us/j/382949597
Abstract:
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.