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Are there classes of algebraic varieties for which algebraic and rational equivalence for algebraic cycles coincide? (references also appreciated)

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    $\begingroup$ For varieties with cellular decompositions, rational=homological equivalence, and therefore algebraic equivalence. See Fulton's intersection theory 19.1.11. This also holds for toric varieties for similar reasons. $\endgroup$
    – Donu Arapura
    Commented Mar 17, 2021 at 12:04
  • $\begingroup$ Over $\bar{\mathbf F}_p$, they agree when you use $\mathbf Q$-coefficients, basically because Jacobians of varieties over finite fields are torsion. $\endgroup$
    – R. van Dobben de Bruyn
    Commented Mar 17, 2021 at 14:21

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