Two Cycle Class Maps on Torsion Cycles

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 α ⁱX CHⁱ(X)_Z→ H²ⁱL(X,Z(i)) restricted to torsion cycles.