Details
| Original language | English |
|---|---|
| Article number | 109972 |
| Number of pages | 45 |
| Journal | Advances in mathematics |
| Volume | 458 |
| Issue number | B |
| Early online date | 15 Oct 2024 |
| Publication status | Published - Dec 2024 |
Abstract
In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.
Keywords
- Higher Chow groups, Homology theory, Refined unramified cohomology
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Advances in mathematics, Vol. 458, No. B, 109972, 12.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Higher Chow groups with finite coefficients and refined unramified cohomology
AU - Kok, Kees
AU - Zhou, Lin
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2024/12
Y1 - 2024/12
N2 - In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.
AB - In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.
KW - Higher Chow groups
KW - Homology theory
KW - Refined unramified cohomology
UR - http://www.scopus.com/inward/record.url?scp=85206256825&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2303.05215
DO - 10.48550/arXiv.2303.05215
M3 - Article
AN - SCOPUS:85206256825
VL - 458
JO - Advances in mathematics
JF - Advances in mathematics
SN - 0001-8708
IS - B
M1 - 109972
ER -