Canonical Witt formal scheme extensions and p-torsion groups

TL;DR

This paper investigates the structure of arithmetic jet spaces of p-torsion subgroups in formal group schemes, revealing a canonical exact sequence involving Witt vectors, generalizing Buium's work on roots of unity.

Contribution

It introduces a new canonical short exact sequence relating jet spaces, Witt vectors, and p-torsion groups in formal schemes, extending previous results.

Findings

Jet spaces fit into a canonical exact sequence involving Witt vectors and p-torsion groups.

Generalizes Buium's results on roots of unity to broader formal group schemes.

Provides structural insights into p-torsion subgroup schemes in formal geometry.

Abstract

We study the $n$-th arithmetic jet space of the $p$-torsion subgroup attached to a smooth commutative formal group scheme. We show that the $n$-th jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length $n$ and the $p$-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity.