The Gersten conjecture for p-adic \'etale Tate twists and the p-adic cycle class map

We prove the Gersten conjecture for p-adic \'etale Tate twists for a smooth scheme X in mixed characteristic. Furthermore, we revisit the cycle class map from thickened zero-cycles on the special fiber of X to \'etale cohomology with coefficients in p-adic \'etale Tate twists previously studied in [13]. The approach we use in this article is more conceptual and works in greater generality.