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Title:cdh descent for homotopy Hermitian K-Theory of rings with involution
Author(s):Carmody, Daniel
Director of Research:Heller, Jeremiah
Doctoral Committee Chair(s):McCarthy, Randy
Doctoral Committee Member(s):Berwick-Evans, Daniel; Rezk, Charles
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2020-07-17
Type:Thesis
URI:http://hdl.handle.net/2142/108490
Rights Information:Copyright 2020 Daniel Carmody
Date Available in IDEALS:2020-10-07
Date Deposited:2020-08


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