Log prismatic $F$-crystals and realization functors

TL;DR

This paper develops realization functors for log prismatic F-crystals, connecting them to other p-adic cohomology theories, especially in cases with boundary divisors involving horizontal components.

Contribution

It constructs and analyzes realization functors from log prismatic F-crystals to other p-adic cohomology coefficient objects, extending the theory to include horizontal boundary divisors.

Findings

Established functors connecting log prismatic F-crystals to other cohomology theories.

Extended the framework to include boundary divisors with horizontal components.

Provided new tools for comparing p-adic cohomology theories.

Abstract

Log prismatic cohomology theory developed by Koshikawa-Yao involves coefficient objects, called log prismatic $F$-crystals. In this paper, we construct and study realization functors from the category of log prismatic $F$-crystals to the category of coefficient objects of other $p$-adic cohomology theories, in the setting where boundary divisors may involve horizontal components.