Green conjectured in his ICM talk 1998 that the rational Chow group of a smooth complex projective variety admits a finite decreasing filtration such that the graded pieces are detected by higher Abel—Jacobi invariants. Green proposed explicit candidates for such invariants, but Voisin showed in 1999 that Green's higher Abel—Jacobi invariants do not quite have the desired properties. It remained open whether a refinement of Green’s maps satisfy Green’s conjecture. In this talk I explain a positive answer to Green’s conjecture for torsion cycles modulo algebraic equivalence: there is a finite decreasing filtration such that the graded pieces are detected by higher Abel—Jacobi invariants.

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