Higher-dimensional arithmetic using p-adic étale Tate twists

Abstract

This paper is a survey on recent researches of the author and his recent joint work with Shuji Saito. We will explain how to construct p-adic étale Tate twists on regular arithmetic schemes with semistable reduction, and state some fundamental properties of those objects. We will also explain how to define cycle class maps from Chow groups to étale cohomology groups with coefficients in p-adic étale Tate twists and state injectivity and surjectivity results on those new cycle class maps.