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Semilocal Milnor K-Theory
International Mathematics Research Notices, Volume: 2023, Issue: 24, Pages: 22069 - 22095
Swansea University Author:
Grigory Garkusha
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© 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.
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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...
| Published in: | International Mathematics Research Notices |
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| ISSN: | 1073-7928 1687-0247 |
| Published: |
Oxford University Press (OUP)
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa61996 |
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| 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-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. |
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| College: |
Faculty of Science and Engineering |
| Funders: |
Swansa University. EPSRC (EP/W012030/1). |
| Issue: |
24 |
| Start Page: |
22069 |
| End Page: |
22095 |