2026-09-23T05:18:01Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/113270 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Heller, Jeremiah McCarthy, Randy Rezk, Charles Stojanoska, Vesna Okano, Tsutomu 2022-01-12T22:54:09Z 2022-01-12T22:54:09Z 2024-01-12T22:56:20Z 2021-07-08 2021-08 Equivariant motivic homotopy theory is a homotopy theory of schemes with algebraic group actions. This thesis is mainly divided into two parts. In the first part, we define four model categories of motivic spectra that present the $\infty$-category $\SH^G(S)$. We use the model categorical setup to reproduce the motivic norm functors, which were originally defined in \cite{BH}. In the second part, we define a theory of orientation in $A$-equivariant motivic homotopy theory, at least for a finite abelian group $A$. As an application, we prove the equivariant motivic analogue of the Snaith theorem $$(\Sigma^\infty_+ \P(\U_A))[\beta^{-1}] \simeq \KGL_A$$ and use it to show that equivariant algebraic $K$-theory is a normed motivic ring spectrum. Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2023-08-01 The student, Tsutomu Okano, accepted the attached license on 2021-07-04 at 03:42. The student, Tsutomu Okano, submitted this Dissertation for approval on 2021-07-04 at 04:16. This Dissertation was approved for publication on 2021-07-08 at 16:52. DSpace SAF Submission Ingestion Package generated from Vireo submission #16754 on 2022-01-12 at 13:03:53 Made available in DSpace on 2022-01-12T22:54:09Z (GMT). No. of bitstreams: 3 OKANO-DISSERTATION-2021.pdf: 759688 bytes, checksum: cf9a9bdb55ebeb7910488f5e7ff81477 (MD5) LICENSE.txt: 4210 bytes, checksum: 25aecbf21c14603a73be15d6c880607c (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 787486f6e750d1224e004ef8dc59f2ac (MD5) Previous issue date: 2021-07-08 Embargo set by: Seth Robbins for item 121197 Lift date: 2024-01-12T22:54:14Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 121197 Lift date: 2024-01-12T22:55:09Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Embargo set by: Seth Robbins for item 121197 Lift date: 2024-01-12T22:56:20Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system Author requested closed access (OA after 2yrs) in Vireo ETD system Limited application/pdf http://hdl.handle.net/2142/113270 en Copyright 2021 Tsutomu Okano Homotopy theory Motivic homotopy theory Algebraic K-theory Algebraic geometry A motivic norm structure on equivariant algebraic K-theory text Thesis Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.