Iwasawa theory for $K(1)$-local spectra
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- by Rebekah Hahn and Stephen Mitchell PDF
- Trans. Amer. Math. Soc. 359 (2007), 5207-5238 Request permission
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.References
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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
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 359 (2007), 5207-5238
- MSC (2000): Primary 55N15, 19L20
- DOI: https://doi.org/10.1090/S0002-9947-07-04204-3
- MathSciNet review: 2327028