Adequate equivalence relations and Pontryagin products

Let A be an abelian variety over a field k. We consider CH0(A) as a ring under Pontryagin product and relate powers of the ideal I⊆CH0(A) of degree zero elements to powers of the algebraic equivalence relation. We also consider a filtration F0⊇F1⊇… on the Chow groups of varieties of the form T×kA (defined using Pontryagin products on A×kA considered as an A-scheme via projection on the first factor) and prove that Fr coincides with the r-fold product (F1)*r as adequate equivalence relations on the category of all such varieties.