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Algebraic cycles on Jacobian varieties

Arnaud Beauville
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Abstract

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 W_1=C, W_2=C+C, ..., W_{g-1}. If C admits a morphism of degree d onto P^1, we prove that the last d-1 classes suffice.

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BibTeXRIS

Arnaud Beauville. 2002-04-15. Algebraic cycles on Jacobian varieties. https://arxiv.org/abs/math/0204188

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