Un anneau de deformation universel en conducteur superieur (A universal deformation ring in higher conductor)

TL;DR

This paper proves that a specific versal deformation ring in higher conductor is actually universal, providing the first example of such a universal deformation ring in this context, with implications for deformation theory.

Contribution

It demonstrates that the versal deformation ring for an automorphism of order 5 with Hasse conductor 2 is universal, the first known example in higher conductor cases.

Findings

The deformation ring is universal, not just versal.

First example of a universal deformation ring in higher conductor.

Advances understanding of deformation rings in algebraic geometry.

Abstract

Let k denote a perfect field of characteristic 5. We show that the versal deformation ring of an element of order 5 and Hasse conductor 2 as automorphism of a ring of formal power series k[[t]] computed by Bertin and Mezard, is in fact universal. This provides the first example of a non trivial universal deformation ring in higher conductor.