Cycle classes for p-adic \'etale Tate twists and the image of p-adic regulators

TL;DR

This paper constructs p-adic étale Chern and cycle class maps, relates them to Bloch-Kato's finite part, and shows the p-adic regulator maps' images lie in this finite part under specific conditions.

Contribution

It introduces new constructions of p-adic étale cycle classes and connects them to the finite part of Galois cohomology, advancing understanding of p-adic regulators.

Findings

Construction of p-adic étale Chern and cycle class maps

Relation established between p-adic Tate twists and Bloch-Kato's finite part

Proof that p-adic regulator maps' images are in the finite Galois cohomology part

Abstract

In this paper, we construct Chern class maps and cycle class maps with values in p-adic \'etale Tate twists [S2]. We also relate the p-adic \'etale 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.