In an article about the life of Grothendieck, available here:

http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf

Allyn Jackson writes about how Mumford was profoundly impressed:

Mumford found the leaps into abstraction to be breathtaking. Once he asked Grothendieck how to prove a certain lemma and got in reply a highly abstract argument. Mumford did not at first believe that such an abstract argument could prove so concrete a lemma. “Then I went away and thought about it for a couple of days, and I realized it was exactly right,” Mumford recalled.

What were the lemma and proof that so impressed Mumford?

(I have tried asking algebraic geometers and category theorists; the tags attached to this question are speculative.)

here(p. 4). $\endgroup$4more comments