## Localization at b₁₀ in the stable category of comodules over the Steenrod reduced powers

##### Author(s)

Belmont, Eva Kinoshita
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##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Haynes Miller.

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Show full item record##### Abstract

Chromatic localization can be seen as a way to calculate a particular infinite piece of the homotopy of a spectrum. For example, the (finite) chromatic localization of a p-local sphere is its rationalization, and the corresponding chromatic localization of its Adams E2 page recovers just the zero-stem. We study a different localization of Adams E2 pages for spectra, which recovers more information than the chromatic localization. This approach can be seen as the analogue of chromatic localization in a category related to the derived category of comodules over the dual Steenrod algebra, a setting in which Palmieri has developed an analogue of chromatic homotopy theory. We work at p = 3 and compute the E2 page and first nontrivial differential of a spectral sequence converging to ... (where P is the Steenrod reduced powers), and give a complete calculation of other localized Ext groups, including ...

##### Description

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 157-159).

##### Date issued

2018##### Department

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

Massachusetts Institute of Technology

##### Keywords

Mathematics.