Toward equivariant Iwasawa theory |
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Authors: | Jürgen Ritter Alfred Weiss |
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Institution: | 1.Institut für Mathematik, Universit?t Augsburg, 86135 Augsburg, Germany. e-mail: ritter@math.uni-augsburg.de,DE;2.Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Canada. e-mail: weissa@ualberta.ca,CA |
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Abstract: | Let l be an odd prime number, K/k a finite Galois extension of totally real number fields, and G
∞
, X
∞
the Galois groups of K
∞
/k and M
∞
/K
∞
, respectively, where K
∞
is the cyclotomic l-extension of K and M
∞
the maximal abelian S-ramified l-extension of K
∞
with S a sufficiently large finite set of primes of k. We introduce a new K-theoretic variant of the Iwasawa ℤG
∞
]]-module X
∞
and, for K/k abelian, formulate a conjecture, which is the main conjecture of classical Iwasawa theory when lłK : k]. We prove this new conjecture when Iwasawa's μ-invariant vanishes and discuss consequences for the Lifted Root Number Conjecture at l.
Received: 7 August 2001 / Revised version: 6 May 2002
We acknowledge financial support provided by NSERC.
Mathematics Subject Classification (2000): 11R23, 11R27, 11R32, 11R33, 11R37, 11R42, 11S20, 11S23, 11S31, 11S40 |
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Keywords: | |
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