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Periodicity in motivic homotopy theory and over BP*BP

dc.contributor.advisorTeichner, Peter
dc.contributor.authorKrause, Achim
dc.date.accessioned2020-04-25T09:23:39Z
dc.date.available2020-04-25T09:23:39Z
dc.date.issued03.07.2018
dc.identifier.urihttp://hdl.handle.net/20.500.11811/7592
dc.description.abstractIn classical homotopy theory, the Periodicity theorem by Devinatz-Hopkins-Smith gives a complete answer as to what types of periodicities can occur in stable homotopy theory. In motivic homotopy theory, there are additional "exotic" periodicities, but a precise classification is unknown. This work is a first step towards such a classification in the stable motivic homotopy category over the complex numbers.
Our approach is to reduce the understanding of periodicity in the motivic homotopy category to corresponding questions in a category of derived comodules over the BP Hopf algebroid, through a theorem of Gheorghe, Wang and Xu. This algebraic question in turn can be inductively reduced to simpler Hopf algebroids.
In addition to the classical family of periodicities and one previously known family of exotic motivic periodicities due to Gheorghe, we are able to show the existence of an infinite number of analogous such families. Corresponding periodic patterns in motivic homotopy groups are discussed. Interesting byproducts of the approach include analogous results in the setting of derived comodules over the BP Hopf algebroid, as well as an explicit periodicity statement about the Adams-Novikov E2 page akin to classical Adams periodicity.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMotivische Homotopietheorie
dc.subjectChromatische Homotopietheorie
dc.subjectHopf-Algebroide
dc.subjectHomologische Algebra
dc.subjectAdams-Spektralfolgen
dc.subjectmotivic homotopy theory
dc.subjectchromatic homotopy theory
dc.subjecthopf algebroids
dc.subjecthomological algebra
dc.subjectAdams spectral sequences
dc.subject.ddc510 Mathematik
dc.titlePeriodicity in motivic homotopy theory and over BP*BP
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-51245
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID5124
ulbbnediss.date.accepted2018-06-26
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeIsaksen, Daniel


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