On the image of the <IMG ALIGN=BOTTOM HEIGHT=14 WIDTH=4>-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Chad Schoen

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

Abstract:	Let be a smooth projective variety of dimension at most 4 defined over the algebraic closure of a finite field of characteristic . It is shown that the Tate conjecture implies the surjectivity of the -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 and almost all . For a special class of threefolds the surjectivity of $mathbf{a}^{2}_{Y,l}$ is proved without assuming any conjectures.

Keywords:	Algebraic cycles $l$-adic Abel-Jacobi map

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