Motivic monodromy and p-adic cohomology theories

TL;DR

This paper develops a unified framework for monodromy and weight filtrations in p-adic cohomology theories, providing new definitions and tools for understanding the cohomology of varieties over local fields.

Contribution

It introduces a log-geometry-free definition of Hyodo-Kato cohomology and constructs an induced Clemens-Schmid chain complex, advancing the study of p-adic cohomology.

Findings

Unified framework for monodromy operators and weight filtrations

Streamlined, log-geometry-free definition of Hyodo-Kato cohomology

Construction of an induced Clemens-Schmid chain complex

Abstract

We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo-Kato cohomology without recourse to log-geometry, as predicted by Fontaine, and we produce an induced Clemens-Schmid chain complex.