2026-09-21T22:38:28Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/116039 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Heller, Jeremiah B Stojanoska, Vesna McCarthy, Randy Rezk, Charles W 2022-08 application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-08-01 The student, Brian Shin, accepted the attached license on 2022-06-24 at 16:36. The student, Brian Shin, submitted this Dissertation for approval on 2022-06-24 at 16:46. This Dissertation was approved for publication on 2022-06-27 at 17:00. DSpace SAF Submission Ingestion Package generated from Vireo submission #18104 on 2022-11-15 at 19:16:46 Norms and transfers in motivic homotopy theory Shin, Brian 2022-06-27 Motivic Homotopy Theory Homotopy Theory Algebraic Geometry 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. Thesis eng https://hdl.handle.net/2142/116039 Copyright 2022 Brian Shin Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics