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

Abstract

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 Griff²(W)/l are infinite for suitable primes l. We further give examples of smooth projective fourfolds W × F over these p-adic fields for which the l-torsion subgroup CH³ (W × F)[l] is infinite.