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.)
Best Answer
The concrete lemma was "The Theorem of The Cube", (Mumford, Abelian Varieties [AV], Section 6) as indicated by Tabes Bridges. The abstract argument was the second theorem in Section 5 of AV (p.46).
In Mumford's collected works, Volume 2, p. 689 there is a letter of Grothendieck to Mumford in which the abstract argument is discussed, and footnote 2 indicates that it was published by Mumford in AV as the second theorem in Chapter 5.
All of this was confirmed in an email correspondence with Mumford.
I am obliged Mumford (of course), to Tabes Bridges for giving the right answer and to Benjamin Dickman for a reminder to post. I should look at MO more frequently!