The term "local field" can refer to different concepts in different contexts, including mathematics, physics, and other fields. Here are two common meanings: 1. **Local Fields in Number Theory**: In the context of algebraic number theory, a local field is a complete field with respect to a discrete valuation, which is often associated with the study of numbers in number fields. These fields are typically used to examine the local properties of arithmetic objects.
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A local field is a nondiscrete locally compact topological field. A non-Archimedean local field is a finite extension of or of .