Two Cycle Class Maps on Torsion Cycles

2024/01/19 by Alexandrou, Theodosis
#14C15 #14C25 (Primary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2401.11014

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 étale motivic cycle class map αⁱ_X\colon CHⁱ(X)_ℤ_ℓ→ H²ⁱ_L(X,ℤ_ℓ(i)) restricted to torsion cycles.

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