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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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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 |