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Proceedings of the London Mathematical Society Advance Access originally published online on June 21, 2007
Proceedings of the London Mathematical Society 2007 95(3):545-566; doi:10.1112/plms/pdm013
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© 2007 London Mathematical Society

Drinfeld modules and torsion in the Chow groups of certain threefolds

Chad Schoen

Department of Mathematics
Duke University
Box 90320
Durham, NC 27708-0320
USA
schoen{at}math.duke.edu

Jaap Top

IWI
University of Groningen
P.O. Box 800
9700 AV Groningen
The Netherlands

Received 13 September 2005. Revision received 19 December 2006.

Let E -> B be an elliptic surface defined over the algebraic closure of a finite field of characteristic greater than 5. Let W be a resolution of singularities of E x B E. We show that the l-adic Abel–Jacobi map from the l-power-torsion in the second Chow group of W to H3(W, Zl(2)){otimes} Ql/Zl is an isomorphism for almost all primes l. A main tool in the proof is the assertion that certain CM-cycles in fibres of W -> B are torsion, which is proven using results from the theory of Drinfeld modular curves.

2000 Mathematics Subject Classification 14C25 (primary), 11G09, 11G16 (secondary).

The first author gratefully acknowledges support from NSA (MDA904-97-1-0041), NSF (DMS-9306733, DMS-9970500, DMS-0200012), and a Duke University Planning Grant for International Research.


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