cdh descent for homotopy Hermitian K-Theory of rings with involution
Carmody, Daniel
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https://hdl.handle.net/2142/108490
Description
Title
cdh descent for homotopy Hermitian K-Theory of rings with involution
Author(s)
Carmody, Daniel
Issue Date
2020-07-17
Director of Research (if dissertation) or Advisor (if thesis)
Heller, Jeremiah
Doctoral Committee Chair(s)
McCarthy, Randy
Committee Member(s)
Berwick-Evans, Daniel
Rezk, Charles
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Algebraic K-Theory
Homotopy Theory
Abstract
We provide a geometric model for the classifying space of automorphism groups of Hermitian vector bundles over a ring with involution with 2 invertible; this generalizes a result of Schlichting-Tripathi. We then prove a periodicity theorem for Hermitian K-theory and use it to construct an E-infinity motivic ring spectrum representing homotopy Hermitian K-theory. From these results, we show that the representing spectrum is stable under base change, and cdh descent for homotopy Hermitian K-theory of rings with involution is a formal consequence.
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