Milnor K-theory, F-isocrystals and Syntomic Regulators

TL;DR

This paper develops a framework connecting Milnor K-theory with F-isocrystals and syntomic cohomology, providing tools for studying syntomic regulators in p-adic Hodge theory.

Contribution

It introduces a category of filtered F-isocrystals and constructs symbol maps compatible with syntomic symbols, advancing the understanding of syntomic regulators.

Findings

Constructed symbol maps on Milnor K-theory

Established compatibility with log syntomic cohomology

Laid groundwork for applications in syntomic regulators

Abstract

We introduce a category of filtered F-isocrystals and construct a symbol maps on Milnor K-theory which is compatible with the syntomic symbol maps to the log syntomic cohomology. These are fundamental materials in our applications on syntomic regulators which we work in other papers.