Equivalence Relations on Algebraic Cycles

Abstract

Algebraic cycles give rise to important invariants of algebraic varieties, and it is common to study the groups of algebraic cycles via so-called adequate equivalence relations. For example, the basic Chow groups are defined by considering cycles modulo rational equivalence. Rational, algebraic, homological and numerical equivalence have been considered since long time, and it is still a most interesting task to understand the precise relationship between them. But there are other adequate equivalence relations, like the l-cubical equivalence which coincides with algebraic equivalence for l = 1.