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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 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
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.
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 well-known conjecture attributed to Bloch and Beilinson:
Conjecture 1.1. For every object X of Vk there exists a descending filtration F


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


Collections: Mathematics