On the image of the 𝑙-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field

Schoen, Chad¹

¹ Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708-0320

Journal of the American Mathematical Society, Tome 12 (1999) no. 3, pp. 795-838

Résumé

Let $Y$ be a smooth projective variety of dimension at most 4 defined over the algebraic closure of a finite field of characteristic $>2$. It is shown that the Tate conjecture implies the surjectivity of the $l$-adic Abel-Jacobi map, $\mathbf {a}^{r}_{Y,l}:CH^{r}_{hom}(Y)\to H^{2r-1}(Y,\mathbb Z_l (r))\otimes \mathbb Q_l /\mathbb Z_l$, for all $r$ and almost all $l$. For a special class of threefolds the surjectivity of $\mathbf {a}^{2}_{Y,l}$ is proved without assuming any conjectures.

Détail

DOI : 10.1090/S0894-0347-99-00303-3

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