{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108490"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108490","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"cdh descent for homotopy Hermitian K-Theory of rings with involution","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Carmody, Daniel"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Heller, Jeremiah","McCarthy, Randy","Berwick-Evans, Daniel","Rezk, Charles"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-10-07T20:59:51Z","date_published":"2020-10-07T20:59:51Z","updated_at":"2026-07-22T22:24:48Z","subjects":["Algebraic K-Theory","Homotopy Theory"],"languages":["en"],"rights":["Copyright 2020 Daniel Carmody"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108490","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Heller, Jeremiah","McCarthy, Randy","Berwick-Evans, Daniel","Rezk, Charles"]},{"key":"dc:creator","label":"Author","values":["Carmody, Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-10-07T20:59:51Z","2020-07-17","2020-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebraic K-Theory","Homotopy Theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Daniel Carmody"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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). 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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). 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