A Field which is complete with respect to a discrete Valuation is called a local field if its Field of Residue Classes is Finite. The Hasse Principle is one of the chief applications of local field theory.

**References**

Iyanaga, S. and Kawada, Y. (Eds.). ``Local Fields.'' §257 in
*Encyclopedic Dictionary of Mathematics.* Cambridge, MA: MIT Press, pp. 811-815, 1980.

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1999-05-25