local field
A local field is a topological field which is Hausdorff and locally compact as a topological space.
Examples of local fields include:
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Any field together with the discrete topology.
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The field of real numbers.
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The field of complex numbers.
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The field of –adic rationals (http://planetmath.org/PAdicIntegers), or any finite extension thereof.
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The field of formal Laurent series in one variable with coefficients in the finite field of elements.
In fact, this list is complete—every local field is isomorphic as a topological field to one of the above fields.
1 Acknowledgements
This document is dedicated to those who made it all the way through Serre’s book [1] before realizing that nowhere within the book is there a definition of the term “local field.”
References
- 1 Jean–Pierre Serre, Local Fields, Springer–Verlag, 1979 (GTM 67).
Title | local field |
---|---|
Canonical name | LocalField |
Date of creation | 2013-03-22 12:48:07 |
Last modified on | 2013-03-22 12:48:07 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13H99 |
Classification | msc 12J99 |
Classification | msc 11S99 |