For a CM elliptic curve E over a number field, the quotient of the n-torsion of the image of the flat pullback on codimension-two cycles by the n-torsion of the model's Chow group is claimed to be pro-finite.
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Selmer group associated to the Chow group of certain codimension two cycles
For a CM elliptic curve E over a number field, the quotient of the n-torsion of the image of the flat pullback on codimension-two cycles by the n-torsion of the model's Chow group is claimed to be pro-finite.