Drinfeld modules and torsion in the Chow groups of certain threefolds

Let E B be an elliptic surface defined over the algebraic closureof a finite field of characteristic greater than 5. Let W bea resolution of singularities of E x _B E. We show that the l-adicAbel–Jacobi map from the l-power-torsion in the secondChow group of W to H³(W, _l(2)) _l/_l is an isomorphism for almostall primes l. A main tool in the proof is the assertion thatcertain CM-cycles in fibres of W B are torsion, which is provenusing results from the theory of Drinfeld modular curves.