Seminars & Colloquia Calendar
Local-global principle for norm over semi-global fields
Sumit Chandra Mishra (Emory U.)
Location: Hill 525
Date & time: Wednesday, 16 October 2019 at 2:00PM - 3:00PM
Abstract: Let K be a complete discretely valued field with residue field kappa. Let F be a function field in one variable over K and X a regular proper model of F with reduced special fibre X a union of regular curves with normal crossings. Suppose that the graph associated to X is a tree (e.g. F = K(t)). Let L/F be a Galois extension of degree n with Galois group G and n coprime to char(kappa). Suppose that kappa is algebraically closed field or a 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 it is a norm from the extensions L otimesF Fnu / Fnu for all discrete valuations nu of F.