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Sep 13, 2017 at 19:33 comment added nfdc23 Read Theorem 1 of webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/… (which concerns smooth varieties!) and then the top of page 97. Historically, this was the first (rather dramatic) use of resolution as a tool to do things (sort of as a black box) even for the study of smooth varieties. Also look at pp. 120-121 of the Grothendieck-Serre correspondence (which shows that Grothendieck also wondered the same thing).
Sep 13, 2017 at 19:12 history asked david mercurio CC BY-SA 3.0