A direct formulation of Dieudonn\'e module theory

TL;DR

This paper introduces a straightforward formulation of Dieudonné module theory by defining modules of Dieudonné elements, providing explicit duality formulas and differential operators to simplify the theory.

Contribution

It presents a new, simplified approach to Dieudonné module theory, making the duality and differential operators more explicit and accessible.

Findings

Explicit formulas for duality in Dieudonné modules

Simplified formulation of Dieudonné module theory

Clear definitions of differential operators in this context

Abstract

We define a Dieudonn\'e module as the module of Dieudonn\'e elements, and set up Dieudonn\'e module theory in a simple way. Under this formulation we give explicit formulae for the duality and the corresponding differential operators.