Abstract |
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We give an example of a projective smooth
surface X over a p-adic field K such that for any prime ℓ different from p, the ℓ-primary torsion subgroup of
CH0(X), the Chow group of 0-cycles on X, is infinite. A key step in the proof is
disproving a variant of the Bloch–Kato conjecture which
characterizes the image of an ℓ-adic regulator map from a higher Chow
group to a continuous étale cohomology of X by using p-adic
Hodge theory. With the aid of the theory of mixed Hodge modules,
we reduce the problem to showing the exactness of the de Rham
complex associated to a variation of Hodge structure, which is
proved by the infinitesimal method in Hodge theory. Another
key ingredient is the injectivity result on the cycle class map
for Chow group of 1-cycles on a proper smooth model of
X over the ring of integers in
K, due to K. Sato and the second
author.
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Keywords
Chow group, torsion 0-cycles on surface
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Mathematical Subject Classification
Primary: 14C25
Secondary: 14G20, 14C30
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Authors
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