On the Grothendieck resolution for a certain finite flat commutative group scheme of order $p^{n}$ over an $\Bbb{F}_{p}$-algebra

TL;DR

This paper investigates the Grothendieck resolution for specific finite flat commutative group schemes of order p^n over an F_p-algebra, contributing to the understanding of their embeddings into smooth group schemes.

Contribution

It provides new insights into the Grothendieck resolution for a particular class of finite flat commutative group schemes of order p^n over F_p-algebras.

Findings

Constructs the Grothendieck resolution for the specified group schemes.

Analyzes the properties of the embedding into smooth group schemes.

Connects the resolution to normal basis problems in group schemes.

Abstract

For any commutative finite flat group scheme, Grothendieck constructed an embedding into some smooth group scheme. This embedding is called the Grothendieck resolution. Let $p$ be a prime number and $n$ a positive integer. In connection with the normal basis problems in the framework of group schemes proposed by Suwa and the author, we consider the Grothendieck resolution for a certain finite flat commutative group scheme of order $p^{n}$ over an $\Bbb{F}_{p}$-algebra.