 
Summary: Adequate equivalence relations and Pontryagin
products
Reza Akhtar
Abstract
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 ×k A (defined using Pontryagin products on A ×k A considered as an
Ascheme via projection on the first factor) and prove that Fr coincides with
the rfold product (F1)r as adequate equivalence relations on the category of
all such varieties.
Keywords: algebraic cycles, Pontryagin product, adequate equivalence relation
AMS classification codes: 14C15, 14C25
1 Introduction
Let k be a field and Vk the category of smooth projective varieties over k. We open
with a wellknown conjecture attributed to Bloch and Beilinson:
Conjecture 1.1. For every object X of Vk there exists a descending filtration F·
on
CHj
