2026-09-23T01:37:27Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/130166 2026-02-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

application/pdf en text Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2027-08-01 The student, Johnson Tan, accepted the attached license on 2025-07-10 at 22:45. The student, Johnson Tan, submitted this Dissertation for approval on 2025-07-10 at 22:57. This Dissertation was approved for publication on 2025-07-16 at 14:11. DSpace SAF Submission Ingestion Package generated from Vireo submission #22499 on 2025-10-25 at 15:53:27 On Hochschild type constructions in motivic homotopy theory Tan, Johnson 2025-07-16 Heller, Jeremiah Stojanoska, Vesna Rezk, Charles Berwick-Evans, Dan Motivic Homotopy eng In the first part we study a motivic analogue of topological Hochschild homology, which we call motivic Hochschild homology, for normed motivic spectra and its interaction with motivic Thom spectra. We show that the normed motivic Thom construction commutes with motivic Hochschild homology and provide a formula in the case that the base of the motivic Thom spectra is a grouplike normed space. In the second part we study a notion of C-motivic spectra with Gm-action and show that various constructions on the ∞-category of C-motivic spectra SH(C) is compatible with this Gm-equivariant structure. As an application we compute the motivic homotopy Gm-fixed points for a class of examples satisfying a motivic B¨okstedt periodicity condition. 2025-08 Text https://hdl.handle.net/2142/130166 Copyright 2025 Johnson Tan Mathematics Mathematics University of Illinois Urbana-Champaign Ph.D. Dissertation