Abstract Motivic Homotopy Theory

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Title: Abstract Motivic Homotopy Theory
Authors: Arndt, Peter
Thesis advisor: Prof. Dr. Markus Spitzweck
Thesis referee: Prof. David Gepner
Abstract: We explore motivic homotopy theory over deeper bases than the spectrum of the integers: Starting from a commutative group object in a cartesian closed presentable infinity category, replacing the usual multiplicative group scheme in motivic spaces, we construct projective spaces, and show that infinite dimensional projective space is the classifying space of the group object. After passage to the stabilization, we construct a Snaith spectrum, calculate the cohomology represented by it for projective spaces and on its rationalization produce Adams operations and a splitting into summands of their eigenspaces.
URL: https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2017021015476
Subject Keywords: motives; homotopy theory; higher categories; K-theory
Issue Date: 10-Feb-2017
License name: Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Unported
License url: http://creativecommons.org/licenses/by-nc-nd/3.0/
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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