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

Preprint

Publication date

19.01.2024

Publication status

E-pub ahead of print