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

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.