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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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References:

[1] Beauville, A.: Quelques remarques sur la transformation de Fourier dans l’anneau de Chow d’une variété abélienne. Algebraic geometry (Tokyo/Kyoto 1982), Lect. Notes Math. 1016, 238-260. Berlin, Heidelberg, New York: Springer 1983
[2] Bloch, S.: Some elementary theorems about algebraic cycles on abelian varieties. Invent. Math.37, 215-228 (1976) · Zbl 0371.14007
[3] Bloch, S., Srinivas, V.: Remarks on correspondences and algebraic cycles. Am. J. Math.105, 1235-1253 (1983) · Zbl 0525.14003
[4] Ceresa, G.:C is not algebraically equivalent toC ? in its Jacobian. Ann. Math.117, 285-291 (1983) · Zbl 0538.14024
[5] Murre, J.-P.: Un résultat en théorie des cycles algébriques de codimension deux. C. R. Acad. Sci. Paris, sér. I,296, 981-984 (1983) · Zbl 0532.14002
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