cdh descent for homotopy Hermitian K-Theory of rings with involution

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Carmody, Daniel

Contributors dc:contributor

• Heller, Jeremiah
• McCarthy, Randy
• Berwick-Evans, Daniel
• Rezk, Charles

• Algebraic K-Theory
• Homotopy Theory

Statement dc:rights

• Copyright 2020 Daniel Carmody

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/108490

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108490