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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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first_indexed 2023-11-14T11:31:23Z
last_indexed 2023-11-14T11:31:23Z
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spelling v2 64985 2023-11-14 Rational enriched motivic spaces ed197f48be683f75e2f9713eb6aad94f Peter Bonart Peter Bonart true false 2023-11-14 MACS 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. E-Thesis Swansea, Wales, UK Triangulated categories of motives, enriched category theory, Rational motivic Gamma spaces 17 10 2023 2023-10-17 10.23889/SUthesis.64985 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Garkusha, Grigory. Doctoral Ph.D EPSRC postgraduate research scholarship EPSRC postgraduate research scholarship 2024-06-12T17:36:34.6943609 2023-11-14T11:20:50.7548803 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Peter Bonart 1 64985__29012__3fbdd57e4dbb404cab3cbacdddfb301c.pdf 2023_Bonart_P.final.64985.pdf 2023-11-14T11:54:53.1818570 Output 904052 application/pdf E-Thesis – open access true Copyright: The Author, Peter Bonart, 2023. Distributed under the terms of a Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0). true eng https://creativecommons.org/licenses/by-sa/4.0/
title Rational enriched motivic spaces
spellingShingle Rational enriched motivic spaces
Peter Bonart
title_short Rational enriched motivic spaces
title_full Rational enriched motivic spaces
title_fullStr Rational enriched motivic spaces
title_full_unstemmed Rational enriched motivic spaces
title_sort Rational enriched motivic spaces
author_id_str_mv ed197f48be683f75e2f9713eb6aad94f
author_id_fullname_str_mv ed197f48be683f75e2f9713eb6aad94f_***_Peter Bonart
author Peter Bonart
author2 Peter Bonart
format E-Thesis
publishDate 2023
institution Swansea University
doi_str_mv 10.23889/SUthesis.64985
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2023-10-17T17:36:32Z
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score 11.0161915

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