Algebra & Number Theory
- Algebra Number Theory
- Volume 1, Number 2 (2007), 163-181.
Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles
We give an example of a projective smooth surface over a -adic field such that for any prime different from , the -primary torsion subgroup of , the Chow group of -cycles on , is infinite. A key step in the proof is disproving a variant of the Bloch–Kato conjecture which characterizes the image of an -adic regulator map from a higher Chow group to a continuous étale cohomology of by using -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 -cycles on a proper smooth model of over the ring of integers in , due to K. Sato and the second author.
Algebra Number Theory, Volume 1, Number 2 (2007), 163-181.
Received: 30 January 2007
Revised: 15 August 2007
Accepted: 15 September 2007
First available in Project Euclid: 20 December 2017
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Asakura, Masanori; Saito, Shuji. Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles. Algebra Number Theory 1 (2007), no. 2, 163--181. doi:10.2140/ant.2007.1.163. https://projecteuclid.org/euclid.ant/1513797126