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

##### Author(s)

French, Jennifer E
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Mark Behrens.

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Show full item record##### 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.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 71-73).

##### Date issued

2010##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.