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

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 ...

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Belmont, Eva Kinoshita

Advisor dc:contributor.advisor

• Haynes Miller.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/117884

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/117884