Ideal-adic completion of quasi-excellent rings (after Gabber)
  In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura. As a corollary, we establish that an ideal-adic completion of an excellent (resp. quasi-excellent) ring is excellent (resp. quasi-excellent). 
Kazuhiko Kurano, Kazuma Shimomoto
math.AC math.AG