Syntomic complexes and $p$-adic \'etale Tate twists

TL;DR

This paper establishes a connection between syntomic complexes and $p$-adic étale Tate twists on regular schemes, extending the theory to a broader class called $F$-smooth schemes and deriving new results on prismatic cohomology.

Contribution

It identifies syntomic complexes with $p$-adic étale Tate twists on regular schemes and introduces the concept of $F$-smooth schemes to generalize the framework.

Findings

Identification of syntomic complexes with $p$-adic étale Tate twists

Extension of methods to $F$-smooth schemes

New results on absolute prismatic cohomology of regular schemes

Abstract

The primary goal of this paper is to identify syntomic complexes with the $p$-adic \'etale Tate twists of Geisser--Schneider--Sato on regular $p$-torsionfree schemes. Our methods apply naturally to a broader class of schemes that we call "$F$-smooth". The $F$-smoothness of regular schemes leads to new results on the absolute prismatic cohomology of regular schemes.