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Adequate equivalence relations and Pontryagin Reza Akhtar

Summary: Adequate equivalence relations and Pontryagin
Reza Akhtar
Let A be an abelian variety over a eld k. We consider CH 0 (A) as a
ring under Pontryagin product and relate powers of the ideal I  CH 0 (A) of
degree zero elements to powers of the algebraic equivalence relation. We also
consider a ltration F 0  F 1  : : : on the Chow groups of varieties of the
form T  k A (de ned using Pontryagin products on A  k A considered as an
A-scheme via projection on the rst factor) and prove that F r coincides with
the r-fold product (F 1 ) r as adequate equivalence relations on the category of
all such varieties.
Keywords: algebraic cycles, Pontryagin product, adequate equivalence relation
AMS classi cation codes: 14C15, 14C25
1 Introduction
Let k be a eld and V k the category of smooth projective varieties over k. We open
with a well-known conjecture attributed to Bloch and Beilinson:
Conjecture 1.1. For every object X of V k there exists a descending ltration F  on
CH j (X; Q) = CH j


Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)


Collections: Mathematics