Higher Chow groups with finite coefficients and refined unramified cohomology

authored by

Kees Kok, Lin Zhou

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.

Organisation(s)

Institute of Algebraic Geometry

External Organisation(s)

University of Amsterdam
Academy of Mathematics and System Sciences

Type

Article

Journal

Advances in mathematics

Volume

458

No. of pages

45

ISSN

0001-8708

Publication date

12.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2303.05215 (Access: Open)
https://doi.org/10.1016/j.aim.2024.109972 (Access: Open)