@Kevin "@Chuck: what do you think people did before Hartshorne was written? :-) " If they were smart,they studied topology instead,Kevin.........LOL
]]>I think some of my comments have been misconstrued a bit, perhaps because they are peripheral to the topic at hand. (In other words, I both agree with just about everything you said and also agree that your remarks are more on point than what I was saying.) I was indicating that a lot of algebraic geometry throughout the 60s and 70s -- even by superstars like Shimura, Lang, Neron, and so forth -- was not couched in the scheme-theoretic language at all. So I am skeptical about the idea that there was ever an entire generation of students who learned algebraic geometry by reading EGA, at least if you do not construe "algebraic geometry" too narrowly. (Think of Griffiths and Harris, written at about the same time as Hartshorne and not long after the completion of EGA: this is another enormous algebraic geometry book which is remarkably close to being completely disjoint from EGA.) Obviously if you want to restrict to "EGA-style algebraic geometry" then EGA becomes a canonical text.
If anyone cares about my opinion on the subject (and I'm not sure that you should): as a wannabe arithmetic geometer, I often did not find Hartshorne to be speaking my language. Given all the trouble that one takes to set up the edifice of scheme-theoretic algebraic geometry [here at UGA we cover about one chapter of Hartshorne per semester course, so one course on classical geometry, one course on schemes, one on sheaf cohomology and so forth], to dismiss the study of schemes over non-algebraically closed fields as being somehow too complicated seems very weird to me. My favorite books on the subject are Mumford's Red Book and Qing Liu's relatively new text, which I think has a chance to become the Hartshorne-for-arithmetic-geometers of the future. I have nothing against EGA whatsoever: I just happen not to have read it. But I'm not averse to it nor would I warn anyone else off: as a graduate student I found myself having to learn some material out of SGAVII, and I found it to be thoroughly solid and reliable. If I ever needed to know something and someone told me to look it up in EGA, I would do so happily.
]]>I wasn't there to see it myself, even less than Kevin was (he was born in the late 60's, me in the mid 70's), which is why I keep using the word "guess". My evidence is that I have come across papers in or near algebraic geometry by fantastic mathematicians of the period which are just not written with any acknowledgment of the EGA revolution. The two examples that come most immediately to mind are Shimura and Lang, each of whom wrote for decades afterwards without really adopting the scheme-theoretic language. (Don't be too quick to say that they were not algebraic geometers. I think they definitely were, just not of the Grothendieck-Mumford school.) If such luminaries could get away without using EGA-style geometry, I'm thinking that many lesser -- and less fashionable -- students and researchers did the same.
P.S.: Mumford's Red Book is a far cry from EGA. For instance, as a graduate student I read through it fairly carefully without any enormous expenditure of time.
]]>I would guess that even in, say, 1970, less than half of the people in the world learning "algebraic geometry" were reading EGA. Or do you think that's not the case?
]]>Also, I've talked to a bunch of people regarding EGA, and I would be happy to pass on what they told me to you, if you email me (contact info available on my webpage in my MO profile).
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