We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves over perfect fields. For example, if k is finitely generated over ℚ and X → C is a quadric fibration of odd relative dimension at least 11, then CH i(X) is finitely generated for i ≤ 4.
@article{bwmeta1.element.doi-10_2478_s11533-009-0043-2,
author = {Cristian Gonz\'alez-Avil\'es},
title = {Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {606-616},
zbl = {1184.14015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0043-2}
}
Cristian González-Avilés. Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves. Open Mathematics, Tome 7 (2009) pp. 606-616. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0043-2/
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