Geodesic
Lubin--Tate extensions, an elementary approach
Izvestiya. Mathematics , Tome 71 (2007) no. 6, pp. 1079-1104.

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We give an elementary proof of the assertion that the Lubin–Tate extension $L\geqslant K$ is an Abelian extension whose Galois group is isomorphic to $U_K/N_{L/K}(U_L)$ for arbitrary fields $K$ that have Henselian discrete valuation rings with finite residue fields. The term ‘elementary’ only means that the proofs are algebraic (that is, no transcedental methods are used [1], pp. 327, 332). 
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Yu. L. Ershov. Lubin--Tate extensions, an elementary approach. Izvestiya. Mathematics , Tome 71 (2007) no. 6, pp. 1079-1104. http://geodesic.mathdoc.fr/item/IM2_2007_71_6_a0/

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