Abstract
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.
Citation
Masanori Asakura. Shuji Saito. "Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles." Algebra Number Theory 1 (2) 163 - 181, 2007. https://doi.org/10.2140/ant.2007.1.163
Information