Description

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

Google Meet Link: http://meet.google.com/hqk-vobu-npc

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.

Google Meet Link: http://meet.google.com/hqk-vobu-npc

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.

Date

Mon, September 14, 2020

Start Time

3:00pm-4:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Sat, September 12, 2020 7:31pm IST