Locally Compact Fields
نویسنده
چکیده
Theorem 1. Let L be a locally compact, nondiscrete topological field. a) Then L is a finite extension of one of the following fields: (i) K = R. (ii) K = Qp. (iii) K = Fp((t)). b) In case (i) L = R or L = C. c) In case (ii) the ramification index e(L/Qp) and residual degree f(L/Qp) are uniquely determined by the abstract field L, and for any given e, f ∈ Z, the number of finite extensions L/Qp of ramification index e and residual degree f is finite and nonempty. d) In case (iii) the residual degree f is determined by the abstract field L, but the ramification index is not. Moreover, every totally ramified extension of Fq((t)) is isomorphic to Fq((t)).
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