Primitive elements in $p$-divisible groups

TL;DR

This paper introduces primitive elements in truncated p-divisible groups, generalizing the concept of points of exact order N from elliptic curves, with the scheme of primitive elements being finite and locally free.

Contribution

It defines primitive elements in arbitrary truncated p-divisible groups and studies their scheme structure, extending classical notions from elliptic curves.

Findings

Primitive elements form a finite, locally free scheme over the base.

Generalization of points of exact order N to broader p-divisible groups.

Framework for analyzing primitive elements in algebraic groups.

Abstract

We introduce the notion of primitive elements in arbitrary truncated $p$-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the "points of exact order $N$," developed by Drinfeld and Katz-Mazur for elliptic curves.