Formal Laurent series in the context of "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 Q_p (where p is any prime number), or the field of formal Laurent series F_q((T)) over a finite field F_q.