Nilpotence theorem for cycles algebraically equivalent to zero, by Vladimir Voevodsky

In this paper we prove that any correspondence from a smooth algebraic variety to itself which is algebraically equivalent to zero is a nilpotent in the ring of correspondences modulo rational equivalence (with rational coefficients). In fact we prove a stronger result which shows that any cycle algebraically equivalent to zero is ``smash-nilpotent'' modulo rational equivalence.

The last section of the paper is purely speculative and contains a discusion of a very strong Nilpotence Conjecture for algebraic cycles.

Vladimir Voevodsky <>