On Hochschild type constructions in motivic homotopy theory
Tan, Johnson
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https://hdl.handle.net/2142/130166
Description
Title
On Hochschild type constructions in motivic homotopy theory
Author(s)
Tan, Johnson
Issue Date
2025-07-16
Director of Research (if dissertation) or Advisor (if thesis)
Heller, Jeremiah
Doctoral Committee Chair(s)
Stojanoska, Vesna
Committee Member(s)
Rezk, Charles
Berwick-Evans, Dan
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
motivic
homotopy
Abstract
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.
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