Otmar Venjakob: On the Iwasawa theory of p-adic Lie extensions

       Autor: Otmar Venjakob
       Titel:  On the Iwasawa theory of p-adic Lie extensions
       Jahr: 2001
       Seiten: 54
       In: Compos. Math. 138, 1-54, 2003 © Kluwer Academic Publishers 2003
       Preprint

        dvi-file   iwasawa.dvi

        pdf-file   iwasawa.pdf

      Abstract: In this paper the new techniques and results concerning the structure theory of modules over non-commutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions K of number fields k ``up to pseudo-isomorphism". In particular, a close relationship is revealed between the Selmer group of abelian varieties, the Galois group of the maximal abelian unramified p-extension of K as well as the Galois group of the maximal abelian outside S unramified p-extension where S is a finite set of certain places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.

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