Local Field

The complete classification of local fields (up to Isomorphism ) is the following: Archimedean local fields ( R, and the Complex Numbers '''C'''. Non-archimedean local fields of characteristic zero: Finite Extension s of the ''p''-adic Number s Q_''p'' . Non-archimedean local fields of characteristic ''p'': finite extensions of the field of Formal Laurent Series F_''q''((''T'')) over a Finite Field F_''q''. NON-ARCHIMEDEAN LOCAL FIELDS For a non-archimedean local field $F$ , the following objects are very important:
	the '''units''' In Its Ring Of Integers <math>\mathcal{O}^ Imes</math> Which Is Its	"http://wwwinformationdelightinfo/information/entry/unit_sphere" class="copylinks">Unit Sphere <math>\{a\in F: a= 1\}</math>,
	:<math>c^{v(a)}	a\mbox{ for all }a\in F</math>

	CATEGORIES ABOUT LOCAL FIELD

	field theory

	algebraic number theory

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