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Local class field theory via Lubin-Tate theory. (English) Zbl 1169.11054

Let \(K\) be a local field with finite residue field. This self-contained expository paper develops local class field theory for \(K\) using the theory of relative Lubin-Tate formal group laws. The approach is similar to that found by K. Iwasawa [Local class field theory. New York: Oxford University Press; Oxford: Clarendon Press (1986; Zbl 0604.12014)], the main difference being that the present author uses the Coleman norm operator for relative Lubin-Tate formal groups, rather than just classical Lubin-Tate formal groups, as in [loc. cit.]. Overall, this paper provides a complete and concise derivation of local class field theory requiring no background beyond the basic properties of local fields.

MSC:

11S31 Class field theory; \(p\)-adic formal groups
11S15 Ramification and extension theory

Citations:

Zbl 0604.12014
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References:

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