Syntomic cycle classes and prismatic Poincar\'e duality

TL;DR

This paper introduces syntomic cycle classes and establishes prismatic Poincaré duality for proper smooth schemes, advancing the understanding of prismatic cohomology in algebraic geometry.

Contribution

It develops the theory of F-gauges over prisms, constructs syntomic cycle classes, and proves a duality theorem in the prismatic setting.

Findings

Established syntomic cycle classes for proper smooth schemes.

Proved prismatic Poincaré duality in the context of algebraic geometry.

Introduced F-gauges over prisms as a new conceptual framework.

Abstract

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