Syntomic cycle classes and prismatic Poincaré duality

Abstract

We introduce $F$-gauges over a prism, construct syntomic cycle classes, and prove the prismatic Poincaré duality for proper smooth schemes.

Minor corrections; replaced the term "cycle map'' with the more appropriate term "Gysin map''; expanded the proof of the Poincaré duality for Hodge cohomology; to appear in Compositio Mathematica