Higher Chow groups with finite coefficients and refined unramified cohomology.(English)Zbl 07945712
Summary: 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.
MSC:
| 14Cxx | Cycles and subschemes |
| 14Fxx | (Co)homology theory in algebraic geometry |
| 19Exx | \(K\)-theory in geometry |
Cite
References:
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