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Rational enriched motivic spaces / Peter Bonart

Swansea University Author: Peter Bonart

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DOI (Published version): 10.23889/SUthesis.64985

Abstract

Rational enriched motivic spaces are introduced and studied in this thesis to provide new models for connective and very effective motivic spectra with rational coefficients. We first study homological algebra for Grothendieck categories of functors enriched in Nisnevich sheaves with specific transf...

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Published: Swansea, Wales, UK 2023
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
Supervisor: Garkusha, Grigory.
URI: https://cronfa.swan.ac.uk/Record/cronfa64985
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Abstract: Rational enriched motivic spaces are introduced and studied in this thesis to provide new models for connective and very effective motivic spectra with rational coefficients. We first study homological algebra for Grothendieck categories of functors enriched in Nisnevich sheaves with specific transfers A. Following constructions of Voevodsky for triangulated categories of motives and framed motivic-spaces, we introduce and study motivic structures on unbounded chain complexes of enriched functors yielding two new models of the triangulated category of big motives with A-tranfers DMA. We next dene enriched motivic spaces as certain enriched functors of simplicial A-sheaves. We then use the properties of enriched motivic spaces and the above reconstruction results to recover SH(k)>0,Q and SHveff(k)Q.
Keywords: Triangulated categories of motives, enriched category theory, Rational motivic Gamma spaces
College: Faculty of Science and Engineering
Funders: EPSRC postgraduate research scholarship