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Derived mapping spaces as models for localizations by Jennifer E. French.

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dc.contributor.advisor Mark Behrens. en_US French, Jennifer E en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2010-10-29T18:38:36Z 2010-10-29T18:38:36Z 2010 en_US 2010 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. en_US
dc.description Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 71-73). en_US
dc.description.abstract This work focuses on a generalization of the models for rational homotopy theory developed by D. Sullivan and D. Quillen and p-adic homotopy developed by M. Mandell to K(1)-local homotopy theory. The work is divided into two parts. The first part is a reflection on M. Mandell's model for p-adic homotopy theory. Reformulating M. Mandell's result in terms of an adjunction between p-complete, nilpotent spaces of finite type and a subcategory of commutative HIF,-algebras, the main theorem shows that the unit of this adjunction induces an isomorphism between the unstable HF, Adams spectral sequence and the HIF, Goerss-Hopkins spectral sequence. The second part generalizes M. Mandell's model for p-adic homotopy theory to give a model for K(1)-localization. The main theorem gives a model for the K(1)- localization of an infinite loop space as a certain derived mapping space of K(1)- local ring spectra. This result is proven by analyzing a more general functor from finite spectra to a mapping space of K -algebras using homotopy calculus, and then taking the continuous homotopy fixed points with respect to the prime to p Adams operations. en_US
dc.format.extent 73 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Derived mapping spaces as models for localizations by Jennifer E. French. en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 671246451 en_US

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