On the image of the $l$-adic Abel-Jacobi map for a variety over the algebraic closure of a finite field
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- by Chad Schoen
- J. Amer. Math. Soc. 12 (1999), 795-838
- DOI: https://doi.org/10.1090/S0894-0347-99-00303-3
- Published electronically: April 23, 1999
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Abstract:
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.References
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Bibliographic Information
- Chad Schoen
- Affiliation: Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708-0320
- Email: schoen@math.duke.edu
- Received by editor(s): June 24, 1997
- Received by editor(s) in revised form: January 5, 1999
- Published electronically: April 23, 1999
- Additional Notes: This research was partially supported by NSF grants DMS-90-14954, DMS-93-06733.
- © Copyright 1999 American Mathematical Society
- Journal: J. Amer. Math. Soc. 12 (1999), 795-838
- MSC (1991): Primary 14C25, 14G15
- DOI: https://doi.org/10.1090/S0894-0347-99-00303-3
- MathSciNet review: 1672878