Sumit Mishra, Emory University

Date and Time: Monday 14 September, 3:00 p.m - 4.00 p.m.

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Speaker: Sumit Mishra, Emory University

Title: Local-global principles for norms over semi-global fields.

Abstract: Let K be a complete discretely valued field with
the residue field \kappa. Let F be the function field of a smooth,
projective, geometrically integral curve over K
and \mathcal{X} be a regular proper model of F such that
the reduced special fibre X is a union of regular curves
with normal crossings. Suppose that the graph associated to
\mathcal{X} is a tree (e.g. F = K(t)).
Let L/F be a Galois extension of degree n such that
n is coprime to \text{char}(\kappa).
Suppose that \kappa is an algebraically closed field or
a finite field containing a primitive n^{\rm th} root of unity.
Then we show that the local-global principle holds for the
norm one torus associated to the extension L/F
with respect to discrete valuations on F, i.e.,
an element in F^{\times} is a norm
from the extension L/F if and only if
it is a norm from the
extensions L\otimes_F F_\nu/F_\nu
for all discrete valuations \nu of F.
Mon, September 14, 2020
Start Time
3:00pm-4:00pm IST
1 hour
Created by
Sat, September 12, 2020 7:31pm IST