Algebraic cycles on products of elliptic curves over p-adic fields

We show that for any odd prime p there is a smooth projective threefold W defined over a p-adic field such that the Chow group CH2(W)/l and the Griffiths group Griff(2)(W)/l are infinite for suitable primes l. We further give examples of smooth projective fourfolds W x F over these p-adic fields for which the l- torsion subgroup CH3(W x F)[l] is infinite.