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On the Iwasawa Theory of p-Adic Lie Extensions

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Compositio Mathematica

Abstract

In this paper, the new techniques and results concerning the structure theory of modules over noncommutative 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 p-extension unramified outside S where S is a certain finite setof places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.

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  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, 69120, Heidelberg, Germany

    Otmar Venjakob

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Venjakob, O. On the Iwasawa Theory of p-Adic Lie Extensions. Compositio Mathematica 138, 1–54 (2003). https://doi.org/10.1023/A:1025413030203

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