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arXiv · 2401.11014

Two Cycle Class Maps on Torsion Cycles

Theodosis Alexandrou
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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.

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Theodosis Alexandrou. 2024-01-19. Two Cycle Class Maps on Torsion Cycles. https://arxiv.org/abs/2401.11014

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