Presque $\mathbf{C}_p$-repr\'esentations et $(\phi,\Gamma)$-modules

TL;DR

This paper explores the relationship between $(,u)$-modules and $C_p$-representations, providing new insights into their dimensions, heights, and full faithfulness properties.

Contribution

It introduces a method to associate almost $C_p$-representations to $(,u)$-modules and computes their key invariants, establishing a full faithfulness result.

Findings

Computed dimensions and heights of the associated representations

Established a full faithfulness result for $B_e$-representations

Linked $(,u)$-modules to almost $C_p$-representations

Abstract

We associate two almost $C_p$-representations to a $(\phi,\Gamma)$-module, and we compute their dimensions and heights. As a corollary, we get a full faithfulness result for $B_e$-representations.