Algebraic Cycles on Jacobian Varieties

  title={Algebraic Cycles on Jacobian Varieties},
  • Published 2002
Let J be the Jacobian of a smooth curve C of genus g, and let A(J) be the ring of algebraic cycles modulo algebraic equivalence on J , tensored with Q. We study in this paper the smallest Q-vector subspace R of A(J) which contains C and is stable under the natural operations of A(J): intersection and Pontryagin products, pull back and push down under multiplication by integers. We prove that this “tautological subring” is generated (over Q) by the classes of the subvarieties W1 = C,W2 = C + C… CONTINUE READING