Exponential maps and explicit formulas
نویسندگان
چکیده
In this section we introduce an exponential homomorphism for the Milnor K -groups for a complete discrete valuation field of mixed characteristics. In general, to work with the additive group is easier than with the multiplicative group, and the exponential map can be used to understand the structure of the multiplicative group by using that of the additive group. We would like to study the structure of Kq(K) for a complete discrete valuation field K of mixed characteristics in order to obtain arithmetic information of K . Note that the Milnor K -groups can be viewed as a generalization of the multiplicative group. Our exponential map reduces some problems in the Milnor K -groups to those of the differential modules Ω OK which is relatively easier than the Milnor K -groups. As an application, we study explicit formulas of certain type.
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