Kato ’ s higher local class field theory
نویسندگان
چکیده
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X)). The main theorem of local class field theory consists of the isomorphism theorem and existence theorem. In this section we consider the isomorphism theorem. An outline of one of the proofs is as follows. First, for the Brauer group Br(K), an isomorphism inv: Br(K) →̃Q/Z is established; it mainly follows from an isomorphism H1(F,Q/Z) →̃Q/Z where F is the residue field of K . Secondly, we denote by XK = Homcont(GK ,Q/Z) the group of continuous homomorphisms from GK = Gal(K/K) to Q/Z. We consider a pairing K ×XK −→ Q/Z
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