All Questions
Tagged with local-fields global-fields
8 questions
2
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0
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130
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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 ...
- 452
1
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256
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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.
...
user163485
2
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0
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111
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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^{\...
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6
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2
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Why is $K_{\upsilon}|K$ 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 $\upsilon$ a prime of $K$. Then ...
- 111
4
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1
answer
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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 ...
- 412
2
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124
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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'...
- 111
2
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433
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Global Artin reciprocity law from Local class field theory
Let $K=\mathbb F_q((t)), p -$ prime ideal in $K$, $\psi_p$ be the local Artin map$K_p^* \to Gal(K_p^{ab}/K_p)=G_p \subset Gal(K^{ab}/K)$. Then I define global Artin map $\psi_K$as product of $\psi_p$, ...
- 71
58
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9
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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 ...
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