Higher Chow groups with finite coefficients and refined unramified cohomology

verfasst von

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.

Organisationseinheit(en)

Institut für Algebraische Geometrie

Externe Organisation(en)

Universiteit van Amsterdam (UvA)
Academy of Mathematics and System Sciences

Typ

Artikel

Journal

Advances in mathematics

Band

458

Anzahl der Seiten

45

ISSN

0001-8708

Publikationsdatum

12.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2303.05215 (Zugang: Offen)
https://doi.org/10.1016/j.aim.2024.109972 (Zugang: Offen)