Two Cycle Class Maps on Torsion Cycles

authored by

Theodosis Alexandrou

Abstract

We compare two cycle class maps on torsion cycles and show that they agree up to a minus sign. The first one goes back to Bloch (1979), with recent generalizations to non-closed fields. The second is the \'etale motivic cycle class map \(\alpha^{i}_{X}\colon \text{CH}^{i}(X)_{\mathbb{Z}_{\ell}}\to H^{2i}_{L}(X,\mathbb{Z}_{\ell}(i))\) restricted to torsion cycles.

Organisation(s)

Institute of Algebraic Geometry

Type

Article

Journal

International Mathematics Research Notices

Volume

2024

Pages

11625–11641

No. of pages

17

ISSN

1073-7928

Publication date

08.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2401.11014 (Access: Open)
https://doi.org/10.1093/imrn/rnae138 (Access: Closed)