Lifting finite self maps of equicharacteristic complete local rings
  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. 
Mahdi Majidi-Zolbanin, Nikita Miasnikov, Lucien Szpiro
math.AC math.AG math.DS