Cycles algébriques sur la jacobienne d'une courbe.

Abstract : The subject of this thesis is the study of the ring of algebraic cycles on theJacobian variety of a smooth curve, tensored with Q. The cycles are studied from the point of view of Beauville's decomposition into eigenspaces for the operators k_* and k^* associated to the homotheties k : x -> kx . More precisely, we are interested in the tautological cycles : those in the smallest subring containing (an embedding of) the curve and closed under the basic operations of intersection, Pontryagin product and the operators k_* and k^*.

The goal of the thesis is the calculation of new relations between cycles modulo algebraic equivalence, depending on linear systems on the curve.

The point of departure for this work is a formula of Elisabetta Colombo and Bert van Geemen for the algebraic class of a pencil (considered as a subvariety of a symmetric product of the curve), from which they deduce certain vanishing results. We extend this formula to linear systems of higher dimension (and to the Chow ring) to obtain further vanishing results.
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Fabien Herbaut. Cycles algébriques sur la jacobienne d'une courbe.. Mathématiques [math]. Université Nice Sophia Antipolis, 2005. Français. ⟨tel-00012015⟩

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