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  • 1.
    Lundström, Patrik
    University West, Department of Technology, Mathematics and Computer Science.
    Self-dual Normal Integral Bases for Infinite Unramified Extensions2002In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 97, no 2, p. 350-367Article in journal (Refereed)
    Abstract [en]

    We prove a generalization to infinite Galois extensions of local fields, of a classical result by Noether on the existence of normal integral bases for finite tamely ramified Galois extensions. We also prove a self-dual normal integral basis theorem for infinite unramified Galois field extensions of local fields with finite residue fields of characteristic different from 2. This generalizes a result by Fainsilber for the finite case. To do this, we obtain an injectivity result concerning pointed cohomology sets, defined by inverse limits of norm-one groups of free finite-dimensional algebras with involution over complete discrete valuation rings.

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