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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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 PDF
J. Amer. Math. Soc. 12 (1999), 795-838 Request permission

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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Additional 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