Generalized class formations and higher class field theory
نویسندگان
چکیده
Kato established higher local reciprocity map (see section 5 and [K1, Th. 2 of §6] (two-dimensional case), [K2, Th. II], [K3, §4]) using in particular this theorem. In this section we deduce the reciprocity map for higher local fields from this theorem and Bloch–Kato’s theorem of section 4. Our approach which uses generalized class formations simplifies Kato’s original argument. We use the notations of section 5. For a complex X · the shifted-by-n complex X [n] is defined as (X [n]) = Xn+q, dX·[n] = (−1)dX· . For a (pro-)finite group G the derived category of G-modules is denoted by D(G).
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