Finiteness theorems for algebraic cycles of small codimension on quadric fibrations over curves
classification
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math.AG
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algebraiccodimensioncurvescyclesfibrationsfinitelyfinitenessgenerated
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We obtain finiteness theorems for algebraic cycles of small codimension on quadric fibrations X over curves over perfect fields k. For example, if k is finitely generated over Q and the fibration has odd relative dimension at least 11, then CH^{i}(X) is finitely generated for i<=4.
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