Abstract: | One considers the structure of the group of the points of a formal group and its Lutz filtration as a Galois module in an
extension without higher ramification of a local field. Making use, on one hand, of Honda's theory on the classification of
formal groups over complete local rings and, on the other hand, of a generalization to formal groups of the Artin-Hasse function,
one constructs effectively an isomorphism between the group of points and some given additive free Galois module. In particular,
in the multiplicative case one gives a new effective proof of Krasner's theorem on the normal basis of the group of principal
units of a local field in extensions without higher ramification.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 182–192, 1987. |