Norms and transfers in motivic homotopy theory

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Shin, Brian

Contributors dc:contributor

• Heller, Jeremiah B
• Stojanoska, Vesna
• McCarthy, Randy
• Rezk, Charles W

• Motivic Homotopy Theory
• Homotopy Theory
• Algebraic Geometry

Statement dc:rights

• Copyright 2022 Brian Shin

Language dc:language

en, eng

Handle dc:identifier

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

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F116039