2026-09-19T23:47:15Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/597812022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Mark Behrens.
French, Jennifer E
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2010-10-29T18:38:36Z
2010-10-29T18:38:36Z
2010
2010
http://hdl.handle.net/1721.1/59781
671246451
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 71-73).
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.
Ph.D.
73 p.
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Derived mapping spaces as models for localizations by Jennifer E. French.
Thesis
application/pdf
false
Publication
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<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.</Abstract>
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