# Fontaine-Laffaille modules and strongly divisible modules

## TL;DR

This paper explores the relationship between Fontaine-Laffaille modules and strongly divisible modules, providing a new proof of Fontaine-Laffaille's main theorem for primes greater than 2 by relaxing some assumptions.

## Contribution

It establishes a connection between Fontaine-Laffaille modules and strongly divisible modules without relying on the main theorem, offering a novel proof for the main theorem of Fontaine-Laffaille.

## Key findings

- New proof of Fontaine-Laffaille's main theorem for p>2
- Relation established between Fontaine-Laffaille and strongly divisible modules
- Relaxation of assumptions in the proof process

## Abstract

In this note, we study the relation between Fontaine-Laffaille modules and strongly divisible modules, without assuming the main theorem of Fontaine-Laffaille (but we need to assume the main results concerning strongly divisible modules). This in particular gives a new proof for the main theorem of Fontaine-Laffaille (for $p>2$).