Fujiwara, Kazuhiro A proof of the absolute purity conjecture (after Gabber). Algebraic geometry 2000, Azumino (Hotaka), 153--183, Adv. Stud. Pure Math., 36, Math. Soc. Japan, Tokyo, 2002.
This article is an edited vesion of O. Gabber's talk on his proof of the absolute purity conjecture of A. Grothendieck given at the $p$-adic conference held in Toulouse in 1994. The details of the proofs given here are supplied by the author following marvelous ideas due to Gabber.