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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Iwasawa theory for $ K(1)$-local spectra


Authors: Rebekah Hahn and Stephen Mitchell
Journal: Trans. Amer. Math. Soc. 359 (2007), 5207-5238
MSC (2000): Primary 55N15, 19L20
Published electronically: June 4, 2007
MathSciNet review: 2327028
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Abstract: The Iwasawa algebra $ \Lambda$ is a power series ring in one variable over the $ p$-adic integers. It has long been studied by number theorists in the context of $ \mathbb{Z}_p$-extensions of number fields. It also arises, however, as a ring of operations in $ p$-adic topological $ K$-theory. In this paper we study $ K(1)$-local stable homotopy theory using the structure theory of modules over the Iwasawa algebra. In particular, for $ p$ odd we classify $ K(1)$-local spectra up to pseudo-equivalence (the analogue of pseudo-isomorphism for $ \lambda$-modules) and give an Iwasawa-theoretic classification of the thick subcategories of the weakly dualizable spectra.


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Additional Information

Rebekah Hahn
Affiliation: 6805 Windhaven Parkway, S126, The Colony, Texas 75056

Stephen Mitchell
Affiliation: Department of Mathematics, University of Washington, P.O. Box 354350, Seattle, Washington 98195-0001

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04204-3
PII: S 0002-9947(07)04204-3
Keywords: K-theory, homotopy theory, Iwasawa algebra
Received by editor(s): June 14, 2005
Published electronically: June 4, 2007
Additional Notes: The second author was supported by a grant from the National Science Foundation
Article copyright: © Copyright 2007 American Mathematical Society