E_1 ring structures in Motivic Hermitian K-theory

Please use this identifier to cite or link to this item:
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018030216685
Open Access logo originally created by the Public Library of Science (PLoS)
Title: E_1 ring structures in Motivic Hermitian K-theory
Authors: López-Ávila, Alejo
Thesis advisor: Prof. Dr. Markus Spitzweck
Thesis referee: Prof. Dr. Oliver Röndigs
Abstract: This 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.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018030216685
Subject Keywords: algebraic topology; homotopy theory; Hermitian; K-theory; infinity categories
Issue Date: 2-Mar-2018
License name: Namensnennung 3.0 Unported
License url: http://creativecommons.org/licenses/by/3.0/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

Files in This Item:
File Description SizeFormat 
thesis_lopez-avila.pdfPräsentationsformat835,81 kBAdobe PDF
thesis_lopez-avila.pdf
Thumbnail
View/Open


This item is licensed under a Creative Commons License Creative Commons