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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.

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