Sur l’anneau de Chow d’une variété abélienne. (French) Zbl 0566.14003

Let A be an abelian variety and CH(A) its Chow ring. In the \({\mathbb{Q}}\)-vector space \(CH(A)\otimes_{{\mathbb{Z}}}{\mathbb{Q}}\), the operators \(k^*\) (for \(k\in {\mathbb{Z}})\) can be simultaneously diagonalized. We describe geometrically some of the eigenspaces, and give an application to the study of algebraic cycles on an abelian threefold.


14C05 Parametrization (Chow and Hilbert schemes)
14K05 Algebraic theory of abelian varieties
14C99 Cycles and subschemes
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