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Norms and transfers in motivic homotopy theory
Shin, Brian
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https://hdl.handle.net/2142/116039
Description
- Title
- Norms and transfers in motivic homotopy theory
- Author(s)
- Shin, Brian
- Issue Date
- 2022-06-27
- Director of Research (if dissertation) or Advisor (if thesis)
- Heller, Jeremiah B
- Doctoral Committee Chair(s)
- Stojanoska, Vesna
- Committee Member(s)
- McCarthy, Randy
- Rezk, Charles W
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- Motivic Homotopy Theory
- Homotopy Theory
- Algebraic Geometry
- Abstract
- We study norm functors in the sense of Bachmann--Hoyois for various $\infty$-categories of correspondences occurring in motivic homotopy theory. We show in particular that the symmetric monoidal structure $\infty$-category of framed correspondence can be refined to a norm monoidal structure, and that the resulting norm monoidal structure on the $\infty$-category of motivic spectra with framed transfers is compatible with the Reconstruction Theorem of Elmanto--Hoyois--Khan--Sosnilo--Yakerson. This yields a recognition principle for normed motivic spectra. We show similar results for various other flavors of transfer, \emph{e.g.} finite syntomic and oriented finite Gorenstein.
- Graduation Semester
- 2022-08
- Type of Resource
- Thesis
- Handle URL
- https://hdl.handle.net/2142/116039
- Copyright and License Information
- Copyright 2022 Brian Shin
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Graduate Dissertations and Theses at Illinois PRIMARY
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