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Semilocal Milnor K-Theory

Grigory Garkusha Orcid Logo

International Mathematics Research Notices, Volume: 2023, Issue: 24, Pages: 22069 - 22095

Swansea University Author: Grigory Garkusha Orcid Logo

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DOI (Published version): 10.1093/imrn/rnac343

Abstract

In this paper, semilocal Milnor K-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor K-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology groups HpZar(k,Z(2))⁠, p⩽1⁠, are computed as semilocal Milnor K...

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Published in: International Mathematics Research Notices
ISSN: 1073-7928 1687-0247
Published: Oxford University Press (OUP) 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa61996
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spelling v2 61996 2022-11-22 Semilocal Milnor K-Theory 7d3826fb9a28467bec426b8ffa3a60e0 0000-0001-9836-0714 Grigory Garkusha Grigory Garkusha true false 2022-11-22 MACS In this paper, semilocal Milnor K-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor K-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology groups HpZar(k,Z(2))⁠, p⩽1⁠, are computed as semilocal Milnor K-theory groups ˆK M2,3−p(k)⁠. The following applications are given: (i) several criteria for the Beilinson–Soulé Vanishing Conjecture; (ii) computation of K4 of a field; (iii) the Beilinson conjecture for rational K-theory of fields of prime characteristic is shown to be equivalent to vanishing of rational semilocal Milnor K-theory. Journal Article International Mathematics Research Notices 2023 24 22069 22095 Oxford University Press (OUP) 1073-7928 1687-0247 20 12 2023 2023-12-20 10.1093/imrn/rnac343 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansa University. EPSRC (EP/W012030/1). 2024-09-16T13:27:02.7193551 2022-11-22T15:36:51.1222087 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Grigory Garkusha 0000-0001-9836-0714 1 61996__26118__ac03d92f95284e9b96512bde924381d7.pdf 61996.VOR.pdf 2022-12-22T11:00:38.5035069 Output 343256 application/pdf Version of Record true © The Author(s) 2022. Published by Oxford University Press and the Society for Experimental Biology. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. true eng https://creativecommons.org/licenses/by/4.0/
title Semilocal Milnor K-Theory
spellingShingle Semilocal Milnor K-Theory
Grigory Garkusha
title_short Semilocal Milnor K-Theory
title_full Semilocal Milnor K-Theory
title_fullStr Semilocal Milnor K-Theory
title_full_unstemmed Semilocal Milnor K-Theory
title_sort Semilocal Milnor K-Theory
author_id_str_mv 7d3826fb9a28467bec426b8ffa3a60e0
author_id_fullname_str_mv 7d3826fb9a28467bec426b8ffa3a60e0_***_Grigory Garkusha
author Grigory Garkusha
author2 Grigory Garkusha
format Journal article
container_title International Mathematics Research Notices
container_volume 2023
container_issue 24
container_start_page 22069
publishDate 2023
institution Swansea University
issn 1073-7928
1687-0247
doi_str_mv 10.1093/imrn/rnac343
publisher Oxford University Press (OUP)
college_str Faculty of Science and Engineering
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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
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description In this paper, semilocal Milnor K-theory of fields is introduced and studied. A strongly convergent spectral sequence relating semilocal Milnor K-theory to semilocal motivic cohomology is constructed. In weight 2, the motivic cohomology groups HpZar(k,Z(2))⁠, p⩽1⁠, are computed as semilocal Milnor K-theory groups ˆK M2,3−p(k)⁠. The following applications are given: (i) several criteria for the Beilinson–Soulé Vanishing Conjecture; (ii) computation of K4 of a field; (iii) the Beilinson conjecture for rational K-theory of fields of prime characteristic is shown to be equivalent to vanishing of rational semilocal Milnor K-theory.
published_date 2023-12-20T13:27:01Z
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score 11.037056

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