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University of Michigan

1. Chen, Ruian. E_?-Rings and Modules in Kan Spectral Sheaves.

Degree: PhD, Mathematics, 2020, University of Michigan

This thesis sets up the foundations of a theory of rings and modules on sheaves of spectra over topological spaces. The theory is based on Kan spectra, which is better behaved sheaf-theoretically, and a rigid smash product on Kan spectra is constructed, and is well-behaved enough for discussing E_∞-rings and their modules. Moreover, this thesis also develops localization on the homotopy category of sheaves of Kan spectra. Using the machinery of localization, the derived category of Kan spectral sheaves is defined and is compatible with the smash product. The main result of the thesis is building a symmetric monoidal structure on the derived category of modules over an E_∞-ring in Kan spectral sheaves. Advisors/Committee Members: Kriz, Igor (committee member), Merlin, Roberto D (committee member), Burns Jr, Daniel M (committee member), Pixton, Aaron (committee member), Wilson, Jennifer Catherine Hinton (committee member).

Subjects/Keywords: spectra; sheaves; sheaves of spectra; spectral algebra; smash product; rings and modules; Mathematics; Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chen, R. (2020). E_?-Rings and Modules in Kan Spectral Sheaves. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/155195

Chicago Manual of Style (16th Edition):

Chen, Ruian. “E_?-Rings and Modules in Kan Spectral Sheaves.” 2020. Doctoral Dissertation, University of Michigan. Accessed November 29, 2020. http://hdl.handle.net/2027.42/155195.

MLA Handbook (7th Edition):

Chen, Ruian. “E_?-Rings and Modules in Kan Spectral Sheaves.” 2020. Web. 29 Nov 2020.

Vancouver:

Chen R. E_?-Rings and Modules in Kan Spectral Sheaves. [Internet] [Doctoral dissertation]. University of Michigan; 2020. [cited 2020 Nov 29]. Available from: http://hdl.handle.net/2027.42/155195.

Council of Science Editors:

Chen R. E_?-Rings and Modules in Kan Spectral Sheaves. [Doctoral Dissertation]. University of Michigan; 2020. Available from: http://hdl.handle.net/2027.42/155195

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