On the crystalline period map

TL;DR

This paper proves the Fontaine-Jannsen conjecture by establishing a crystalline version of the p-adic Poincaré lemma, providing a new approach compared to earlier proofs by other mathematicians.

Contribution

It introduces a novel crystalline p-adic Poincaré lemma that enables a new proof of the Fontaine-Jannsen conjecture.

Findings

Proof of the Fontaine-Jannsen conjecture

Development of a crystalline p-adic Poincaré lemma

Alternative approach to existing proofs

Abstract

The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).