We give a detailed proof of a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work of Nishimura and Nishimura. As a corollary, we establish that an ideal-adic completion of an excellent (resp., quasi-excellent) ring is excellent (resp., quasi-excellent).
To Professor Jun-ichi Nishimura on the occasion of his 70th birthday
"Ideal-adic completion of quasi-excellent rings (after Gabber)." Kyoto J. Math. 61 (3) 707 - 722, September 2021. https://doi.org/10.1215/21562261-2021-0011