Motivic monodromy and p-adic cohomology theories

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.

51 pages. Minor changes to Section 4.7. To appear in JEMS