Lifting finite self maps of equicharacteristic complete local rings

TL;DR

This paper proves that finite self maps of equicharacteristic complete local rings can be lifted to finite self maps of a containing regular local ring, preserving the embedding of spectra.

Contribution

It establishes a lifting property for finite self maps in equicharacteristic complete local rings, extending previous results in the area.

Findings

Finite self maps of A can be lifted to R.

Preservation of the embedding of Spec(A) in Spec(R).

Generalizes known lifting results in equicharacteristic settings.

Abstract

In the spirit of Fakhruddin (arXiv:math/0212208v1) and Szpiro-Bhatnagar (arXiv:1010.2715v1), we show that for an equicharacteristic complete local ring A, with a given embedding of Spec(A) in the prime spectrum Spec(R) of some complete regular local ring R, any finite self map of A can be lifted to a finite self map of R, keeping the given embedding.