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Drinfeld modules and torsion in the Chow groups of certain threefolds
Author(s) -
Schoen Chad,
Top Jaap
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm013
Subject(s) - mathematics , resolution of singularities , torsion (gastropod) , pure mathematics , elliptic curve , gravitational singularity , isomorphism (crystallography) , algebraic closure , algebraic number , algebra over a field , mathematical analysis , medicine , differential algebraic equation , ordinary differential equation , crystal structure , chemistry , surgery , crystallography , differential equation
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 × B E . We show that the l ‐adic Abel–Jacobi map from the l ‐power‐torsion in the second Chow group of W to H 3 ( W , ℤ l (2))⊗ ℚ l /ℤ l 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.