Group Schemes with $\mathbb F_q$-Action

TL;DR

This paper generalizes the equivalence between certain commutative flat group schemes and Dieudonné modules to include group schemes with an $F_q$-action, extending Drinfel'd's construction.

Contribution

It introduces a new equivalence of categories for group schemes with $F_q$-action, broadening the classical Dieudonné theory.

Findings

Established an equivalence of categories for group schemes with $F_q$-action

Extended Drinfel'd's construction to a broader class of group schemes

Generalized Dieudonné module correspondence in characteristic p

Abstract

Via a construction due to V. Drinfel'd, we prove an equivalence of categories, generalizing the equivalence between commutative flat group schemes in characteristic $p$ with trivial Verschiebung and their Dieudonn\'e modules to group schemes with $\mathbb F_q$-action.