2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216859A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is related to finiteness of two arithmetic objects: One is the $p$-primary torsion part of the Chow group in codimension 2 of $X$. Another is an unramified cohomology group of $X$. As an application, for a regular model ${\mathscr X}$ of $X$ over the integer ring of $k$, we show an injectivity result on torsion of a cycle class map from the Chow group in codimension 2 of ${\mathscr X}$ to a new $p$-adic cohomology of ${\mathscr X}$ introduced by the second author, which is a candidate of the conjectural étale motivic cohomology with finite coefficients of Beilinson-Lichtenbaum.53 pages. The title and the notation has been changed, and Appendix B has been addedAlgebraic GeometryNumber Theory14C25, 14G40text