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2 votes
0 answers
130 views

Can global fields be defined as certain topological fields like local fields?

It's known that local fields can be defined as a non-discrete, Hausdorff (equivalently non-indiscrete), locally compact, topological field, which is the same as non-trivial (i.e. neither discrete nor ...
Z Wu's user avatar
  • 452
1 vote
0 answers
256 views

Globalization of a local field

I am reading the paper ''Endoscopic classification of representations of quasi-split unitary groups'' by Chung Pang Mok, and cannot come up with the proof of theorem 7.2.1. Here is the statement. ...
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2 votes
0 answers
111 views

self dual character of local fields and global fields

There are two concepts of self dual character, one is for global and another is for local. Let K be an imaginary quadratic number field, and a Hecke character $\chi : \mathbb{A}_K^{\times}/K^{\...
Yi_Feng's user avatar
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6 votes
2 answers
819 views

Why is Kυ|K separable for a global field K?

I asked this question on math.stackexchange but maybe it fits here better. If not, I apologize in advance and will remove the question. Let K be a global field and υ a prime of K. Then ...
Frida's user avatar
  • 111
4 votes
1 answer
731 views

Reference for: Every local field can be realized as the completion of a global field

It is well known that every local field (i.e. nondiscrete topological field locally compact with respect to the topology) is the completion of some global field. I know the argument, a nice ...
jaycegetz's user avatar
  • 412
2 votes
0 answers
124 views

Property of a derivative in global field

Before posting I want to make it clear that I posted the same question in stack exchange awhile ago (https://math.stackexchange.com/questions/1533814/property-of-derivative-in-a-local-field) but didn'...
Jack Yoon's user avatar
  • 111
2 votes
0 answers
433 views

Global Artin reciprocity law from Local class field theory

Let K=Fq((t)),p prime ideal in K, ψp be the local Artin mapKpGal(Kabp/Kp)=GpGal(Kab/K). Then I define global Artin map ψKas product of ψp, ...
oznd's user avatar
  • 71
58 votes
9 answers
16k views

Learning Class Field Theory: Local or Global First?

I've noticed that there seem to be two approaches to learning class field theory. The first is to first learn about local fields and local class field theory, and then prove the basic theorems about ...
David Corwin's user avatar
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