A -adic Regulator Map and Finiteness Results for Arithmetic Schemes

  • S. Saito

  • K. Sato


A main theme of the paper is a conjecture of Bloch-Kato on the image of -adic regulator maps for a proper smooth variety over an algebraic number field . The conjecture for a regulator map of particular degree and weight is related to finiteness of two arithmetic objects: One is the -primary torsion part of the Chow group in codimension 2 of . Another is an unramified cohomology group of . As an application, for a regular model of over the integer ring of , we prove an injectivity result on the torsion cycle class map of codimension 2 with values in a new -adic cohomology of introduced by the second author, which is a candidate of the conjectural étale motivic cohomology with finite coefficients of Beilinson-Lichtenbaum.