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In mathematics, a field K is called a non-Archimedean local field if it is complete with respect to a metric induced by a discrete valuation v and if its residue field k is finite. In general, a local field is a locally compact topological field with respect to a non-discrete topology.
It is easily seen that if | · | is non-archimedean and x, y ∈ K with |x| < |y|, then |x + y| = max(|x|, |y|) = |y|. Two absolute values on a field are said to be equivalent if they define the same topology. | · | is called the trivial absolute value on K if |x| = 1 for all x 6= 0. Example.
The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field.
20 de dic. de 2014 · A field that is complete with respect to a discrete valuation and has finite residue field. The structure of a local field $K$ is well known: 1) if the characteristic of $K$ is $0$, then $K$ is a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers; 2) if the characteristic of $K$ is greater than $0$, then $K$ is ...
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Lower.com Field is a multi-purpose stadium in Columbus, Ohio, home to the Columbus Crew and host to various events.
