From: Kevin Buzzard
To: xxxx@xxxx
Subject: [Algebraic_geometry] stuff
Date: Fri, 22 Jul 2005 11:44:13 +0100 (BST)
Reply-To: Kevin Buzzard
Sender: xxxx@xxxx
Hi Johan et al. Here's why I think this project won't work *yet*, and feel
free to prove me wrong!
I think the analogy with the linux kernel has one severe deficiency,
and that is that Torvalds started the linux project not by setting
up a mailing list and saying "hey everyone, let's write a
unix system for a PC, OK let's go"---he didn't do this at all. He wrote
[if I understand the history correctly] tens of thousands of lines of
code, by himself, and he wrote and he wrote until he had a basic version
of a kernel up and running which actually worked. It didn't do everything,
but it did do enough to essentially (just) call itself an operating
system. Then, and only then, did he tell the wider community that he had
done what he had done, and he invited other people to join in. Because the
basic kernel was already there, and lots of people were using unix already,
and lots of those people also had access to PCs, they then tried to get
linux working on their PC for fun or for other reasons, and for some people
it will have worked, and for some it will have nearly worked, and some of
these people will have then been motivated to tinker with
the source until it did work, and for some it will have worked but their
favourite app will not have worked, so this motivated some people to
expand the source to include new functionality so that their favourite
apps worked, and so on.
My understanding is that, apart from the discussions on licenses, the
topics discussed on this mailing list so far indicate that there are still
(in some sense) decisions to be made as to what the final document should look
like---whether it should be an introduction for the grad student who
doesn't know what a locally ringed space is, or whether it should start
with 50 pages of abstract nonsense about morphisms of topoi and then
start the non-formal stuff, or whether it should assume that you have read
EGA1 but not done the masses of implied exercises in Deligne-Mumford,
or... . Everyone has opinions and, almost by definition, Johan's are the
most important because this is his baby (more precisely, one of his babies).
So here is a conjecture about what the situation will be in 6 months time
on this project: there will have been discussions about licenses, some
more debates about whether to include Noetherian hypotheses, with some
people saying that they are essential in certain cases to avoid having to
write 100 pages a la EGA IV sections 8--13 which very few people will ever
read, and with others saying that
it's essential not to have them because of some technical issues with
forming Pic^0 of Neron models and doing Weil descent, when you have to
deal with functors represented by algebraic spaces over bases like
W(F_p-bar) tensor_{Z_p} W(F_p-bar), and there will be technical
discussions and it will be very interesting watching them all go by. But
in the end, we will all have had some fun in this algebraic
geometry chat-room but nothing, or very little, will actually have been
written.
I also conjecture that essentially the *only* way that my pessimistic
prediction above will fail is that Johan himself stops doing his research
and spends 6 months writing version 0 of the *entire book*. I don't know
whether he is prepared to do this. But I feel that this is absolutely key
because it is the unique way to give concrete direction to the project.
Otherwise every 2 weeks people will join the list and then ask the same
questions about whether all schemes are Noetherian, whether you are doing
Deligne-Mumford stacks or Artin stacks, whether you want the book to look
like Hartshorne's book or Illusie's thesis, and so on and so on. Of course
Johan can just give his opinions on all these questions, week after week
after week, but if he just sits down and writes several hundred pages by
himself then whenever anyone asks a question like this, he can just point
to the book and say "that's what I think it should be like, you go ahead
and add some more stuff if you think differently". If suddenly the
200-page document is there, then suddenly the analogue with kernel.org
becomes *much* better, because then there are people out there who want to
give the book to their graduate students so their grad students can learn
about stacks, but what they really want the grad students to learn about
is some specific thing which isn't covered in the book, so the advisor is
motivated to write 10 pages on this specific thing and add them to the
book, because all the groundwork and notation and basic definitions are
already there.
That's what I think :-)
Kevin
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