Lutz filtration as Galois module in an extension without higher ramification

S. V. Vostokov

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 8, Tome 160 (1987), pp. 182-192

Résumé

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.