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E_1 ring structures in Motivic Hermitian K-theory

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018030216685
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dc.contributor.advisorProf. Dr. Markus Spitzweck
dc.creatorLópez-Ávila, Alejo
dc.date.accessioned2018-03-02T15:12:30Z
dc.date.available2018-03-02T15:12:30Z
dc.date.issued2018-03-02T15:12:30Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018030216685-
dc.description.abstractThis Ph.D. thesis deals with E1-ring structures on the Hermitian K-theory in the motivic setting, more precisely, the existence of such structures on the motivic spectrum representing the hermitianK-theory is proven. The presence of such structure is established through two different approaches. In both cases, we consider the category of algebraic vector bundles over a scheme, with the usual requirements to do motivic homotopy theory. This category has two natural symmetric monoidal structures given by the direct sum and the tensor product, together with a duality coming from the functor represented by the structural sheaf. The first symmetric monoidal structure is the one that we are going to group complete along this text, and we will see that the second one, the tensor product, is preserved giving rise to an E1-ring structure in the resulting spectrum. In the first case, a classic infinite loop space machine applies to the hermitian category of the category of algebraic vector bundles over a scheme. The second approach abords the construction using a new hermitian infinite loop space machine which uses the language of infinity categories. Both assemblies applied to our original category have like output a presheaf of E1-ring spectra. To get an spectrum representing the hermitian K-theory in the motivic context we need a motivic spectrum, i.e, a P1-spectrum. We use a delooping construction at the end of the text to obtain a presheaf of E1-ring P1-spectra from the two presheaves of E1-ring spectra indicated above.eng
dc.rightsNamensnennung 3.0 Unported-
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/-
dc.subjectalgebraic topologyeng
dc.subjecthomotopy theoryeng
dc.subjectHermitianeng
dc.subjectK-theoryeng
dc.subjectinfinity categorieseng
dc.subject.ddc510 - Mathematik
dc.titleE_1 ring structures in Motivic Hermitian K-theoryeng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2017-03-27-
dc.contributor.refereeProf. Dr. Oliver Röndigs
dc.subject.bk31.61 - Algebraische Topologie
dc.subject.bk31.62 - Kategorielle Topologie
dc.subject.msc19-02 - Research exposition
dc.subject.msc18-02 - Research exposition
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