Norms and transfers in motivic homotopy theory

Shin, Brian

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https://hdl.handle.net/2142/116039 Copy

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

Copyright and License Information

Copyright 2022 Brian Shin

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