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Topological Quillen Localization and Homotopy Pro-Nilpotent Structured Ring Spectra

Zhang, Yu
http://rave.ohiolink.edu/etdc/view?acc_num=osu1586210485665844

Abstract Details

2020, Doctor of Philosophy, Ohio State University, Mathematics.
The aim of this paper is two-fold: (i) to establish the associated TQ-local homotopy theory for algebras over a spectral operad O as a left Bousfield localization of the usual model structure on O-algebras, which itself is almost never left proper, in general, and (ii) to show that every homotopy pro-nilpotent structured ring spectrum is TQ-local. Here, TQ is short for topological Quillen homology, which is weakly equivalent to O-algebra stabilization. As an application, we simultaneously extend the previously known connected and nilpotent TQ-Whitehead theorems to a homotopy pro-nilpotent TQ-Whitehead theorem. We also compare TQ-localization with TQ- completion and show that TQ-local O-algebras that are TQ-good are TQ-complete. Finally, we show that every (−1)-connected O-algebra with a principally refined Postnikov tower is TQ-local, provided that O is (−1)-connected.
John Harper (Advisor)
Niles Johnson (Committee Member)
Crichton Ogle (Committee Member)
74 p.
Mathematics
structured ring spectra; completion and localization; operad; topological Andre-Quillen homology

Recommended Citations

Citations

  • Zhang, Y. (2020). Topological Quillen Localization and Homotopy Pro-Nilpotent Structured Ring Spectra [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586210485665844

    APA Style (7th edition)

  • Zhang, Yu. Topological Quillen Localization and Homotopy Pro-Nilpotent Structured Ring Spectra. 2020. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1586210485665844.

    MLA Style (8th edition)

  • Zhang, Yu. "Topological Quillen Localization and Homotopy Pro-Nilpotent Structured Ring Spectra." Doctoral dissertation, Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1586210485665844

    Chicago Manual of Style (17th edition)

osu1586210485665844
265
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This open access ETD is published by The Ohio State University and OhioLINK.