Two Cycle Class Maps on Torsion Cycles

Author:

Alexandrou Theodosis1

Affiliation:

1. Institute of Algebraic Geometry, Leibniz University Hannover , Welfengarten 1, 30167 Hannover , Germany

Abstract

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 [6], with recent generalizations to non-closed fields. The second is the étale motivic cycle class map $\alpha ^{i}_{X}\colon \operatorname{CH}^{i}(X)_{{\mathbb{Z}}_{\ell }}\to H^{2i}_{L}(X,{\mathbb{Z}}_{\ell }(i))$ restricted to torsion cycles.

Funder

European Research Council

European Union’s Horizon 2020 research and innovation programme

Publisher

Oxford University Press (OUP)

Reference35 articles.

1. Torsion in Griffiths groups;Alexandrou

2. On Bloch’s map for torsion cycles over non-closed fields;Alexandrou;Forum. Math. Sigma,2023

3. Letter to C;Beilinson;Soulé,1982

4. The pro-étale topology of schemes;Bhatt;Astérisque,2015

5. Roitman’s theorem for singular projective varieties;Biswas;Compos. Math.,1999

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