Cycle classes for $p$-adic étale Tate twists and the image of $p$-adic regulators

Abstract

In this paper, we construct Chern class maps and cycle class maps with values in $p$-adic étale Tate twists citeS2. We also relate the $p$-adic étale Tate twists with the finite part of Bloch-Kato. As an application, we prove that the integral part of $p$-adic regulator maps has values in the finite part of Galois cohomology under certain assumptions.