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Heller, Jeremiah McCarthy, Randy Berwick-Evans, Daniel Rezk, Charles Carmody, Daniel 2020-10-07T20:59:51Z 2020-10-07T20:59:51Z 2020-07-17 2020-08 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms The student, Daniel Carmody, accepted the attached license on 2020-07-14 at 13:39. The student, Daniel Carmody, submitted this Dissertation for approval on 2020-07-14 at 13:41. This Dissertation was approved for publication on 2020-07-17 at 11:43. DSpace SAF Submission Ingestion Package generated from Vireo submission #15610 on 2020-10-02 at 15:13:23 Made available in DSpace on 2020-10-07T20:59:51Z (GMT). No. of bitstreams: 3 CARMODY-DISSERTATION-2020.pdf: 381301 bytes, checksum: 3adbd85e927acfb410c923febb19e4ab (MD5) LICENSE.txt: 4211 bytes, checksum: 40cb609fa998f5de7687f6f337e346f2 (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 631171a0928ce065260104f6f70adf38 (MD5) Previous issue date: 2020-07-17 application/pdf http://hdl.handle.net/2142/108490 en Copyright 2020 Daniel Carmody Algebraic K-Theory Homotopy Theory cdh descent for homotopy Hermitian K-Theory of rings with involution text Thesis Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.