p-adic periods and derived de Rham cohomology

TL;DR

This paper constructs a p-adic period map using derived de Rham cohomology and provides a simple proof of Fontaine's C_{dR} conjecture, advancing understanding in p-adic Hodge theory.

Contribution

It introduces a novel construction of p-adic period maps via derived de Rham cohomology and offers a simplified proof of a major conjecture.

Findings

Construction of p-adic period map using derived de Rham cohomology

Simplified proof of Fontaine's C_{dR} conjecture

Enhanced understanding of p-adic Hodge structures

Abstract

We construct p-adic period map using derived de Rham cohomology of Illusie and give a simple proof of Fontaine's C_{dR} conjecture.