Displayed equations for Galois representations

TL;DR

This paper describes Galois representations linked to p-divisible groups and finite flat p-group schemes using Dieudonné displays and Breuil-Kisin modules, connecting algebraic structures with Galois actions.

Contribution

It provides a unified framework for understanding Galois representations via displays and modules, extending previous results to arbitrary characteristic.

Findings

Galois representations are characterized through Dieudonné displays.

Corollary relates Kisin's description to arbitrary characteristic.

Provides a new perspective on p-adic Galois representations.

Abstract

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic Kisin's description of the Galois representation associated to a commutative finite flat p-group scheme over a p-adic discrete valuation ring in terms of its Breuil-Kisin module. This was obtained earlier by W. Kim by a different method.