Local class field theory in the context of Local field

Local class field theory in the context of Local field

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⭐ Core Definition: Local class field theory

In mathematics, local class field theory (LCFT), introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite residue field: hence every local field is isomorphic (as a topological field) to the real numbers R, the complex numbers C, a finite extension of the p-adic numbers Qp (where p is any prime number), or the field of formal Laurent series Fq((T)) over a finite field Fq.

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Local class field theory in the context of Helmut Hasse

Helmut Hasse (German: [ˈhasə]; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions.

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← Helmut Hasse
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Mathematics → Helmut Hasse → Abelian extension → Local field → Absolute value (algebra) → Discrete valuation → Residue field → Isomorphic → Topological field → Real numbers → Complex numbers → Finite extension → P-adic number → Prime number → Formal Laurent series → Finite field →