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Cohomology of Finite Groups: Basic Properties Read chapter Read first chapter

2020 | OriginalPaper | Chapter

7. Basic Facts About Local Fields

Author : David Harari

Published in: Galois Cohomology and Class Field Theory

Publisher: Springer International Publishing

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Abstract

This chapter recalls basic facts on local fields.

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previous chapter First Notions of Galois Cohomology
next chapter Brauer Group of a Local Field
Footnotes
1
Recall that, by definition this implies in particular that A is an integral domain.
 
2
This definition is not universal, some authors consider \(\mathbf{R}\) and \(\mathbf{C}\) to be local fields, or do not require the residue field to be finite. The definition we adopt here is more common and better suited for number theoretic question.
 
3
Sometimes one says w extending v, but it is important to note that in the case of a ramified extension, one can not ask that w takes values in \(\mathbf{Z}\cup \{ + \infty \}\) and that at the same time the restriction of w to K is equal to v, see Remark 7.9 below.
 
Metadata
Title
Basic Facts About Local Fields
Author
David Harari
Copyright Year
2020
Book
Galois Cohomology and Class Field Theory

Print ISBN: 978-3-030-43900-2

Electronic ISBN: 978-3-030-43901-9

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-43901-9_7

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