
EGA Chapter 1: The Language of Schemes - chmaynard
https://golem.ph.utexas.edu/category/2020/02/ega1_the_language_of_schemes.html
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QuesnayJr
Some background, for those unfamiliar with this area. Algebraic geometry grew
out of the study of solutions of systems of polynomial equations. This is
naturally a question of geometry, which can be studied analytically (using
tools from calculus, for example). If you are willing to consider solutions
over the complex numbers, and not just the real numbers, you can study the
question algebraically, as well. Once you take that step, you can ask what
happens when you look at solutions over exotic objects such as finite fields
or rational functions.

Alexander Grothendieck pushed for a very general formulation of this algebraic
approach, using the notion of "scheme". Together with Jean Dieudonne, he wrote
an introduction to this topic, called EGA, which is French for "Elements of
Algebraic Geometry". This is one of the foundational texts in algebraic
geometry now.

At some point, Grothendieck became disillusioned with both mathematics and
academia, quit both, and isolated himself from most people. Not long before
his death, he expressed the desire that all of his work cease to be published.
He died 5 years ago now, and I'm not actually sure of the legal status of
republishing his work, though people are determined to go ahead because of its
great historical significance. While I think EGA has largely been superseded
by newer sources, some of his later work (known as SGA) has not.

~~~
hackernewsname
>While I think EGA has largely been superseded by newer sources, some of his
later work (known as SGA) has not

Can you elaborate what you mean by “superseded by”?

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QuesnayJr
I just mean that the content can be found from later sources, such as
Hartshorne or the Stacks Project. For some parts of SGA, it is my impression
that literally the only reference is SGA.

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wolfgke
A question to the experts: Of EGA I, there exist two editions:

1\. the 1960 edition, which is available at
[http://www.numdam.org/item/?id=PMIHES_1960__4__5_0](http://www.numdam.org/item/?id=PMIHES_1960__4__5_0)

2\. the 1971 edition: mentioned under
[https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_g%C3%A9o...](https://en.wikipedia.org/wiki/%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique#Bibliographic_information)

As I see it, this translation seems to be of the (older) 1960 edition. Does
anybody know the reason why the translators chose the 1960 edition over the
1971 edition as the translation source?

~~~
orbifold
Grothendieck left IHES in 1970, the second edition was after that. There was a
lot of drama in the aftermath, essentially Grothendieck was not happy about
how the more advanced material (SGA 4) he lectured on was kept private to the
small group of students that attended the seminar and later reappeared in
their publications without much acknowledgement. The eventual SGA 4.5 was a
butchered version that only contained enough background to cover Deligne‘s
proof.

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heinrichhartman
Did Grothendieck himself not explicitly object to any re-publishing or
translation of his manuscripts?

[https://tqft.net/misc/Grothendieck's%20Declaration.pdf](https://tqft.net/misc/Grothendieck's%20Declaration.pdf)

``` Declaration of intent of non-publication

I do not intend to publish or republish any work or text of which I am the
author, in any form whatsoever, printed or electronic, whether in full or in
excerpts, texts of personal nature, of scientific character, or otherwise, or
letters addressed to anybody, and any translation of texts of which I am the
author. Any edition or dissemination of such texts which have been made in the
past without my consent, or which will be made in the future and as long as I
live, is against my will expressly specified here and is unlawful in my eyes.
As I learn of these, I will ask the person responsible for such pirated
editions, or of any other publication containing without permission texts from
my hand (beyond possible citations of a few lines each), to remove from
commerce these books; and librarians holding such books to remove these books
from those libraries.

If my intentions, clearly expressed here, should go unheeded, then the shame
of it falls on those responsible for the illegal editions, and those
responsible for the libraries concerned (as soon as they have been informed of
my intention).

Written at my home, January 3, 2010,

Alexandre Grothendieck. ```

~~~
auntienomen
There comes a point at which a book belongs more to its readers than to its
author. EGA is well past that point. Try imagining the world we'd live in now
if Euclid had managed to suppress all copies of his _Geometry_.

~~~
wolfgke
> There comes a point at which a book belongs more to its readers than to its
> author. EGA is well past that point. Try imagining the world we'd live in
> now if Euclid had managed to suppress all copies of his _Geometry_.

Tell this to the politicians who created the copyright laws.

~~~
JadeNB
> Tell this to the politicians who created the copyright laws.

I am sure Grothendieck would be on the front lines of those castigating such
politicians. He made this request not to ensure personal gain, but to express
his profound disappointment with and disengagement from society as he saw it.

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bordercases
Did we really just get an English translation now?

~~~
aidenn0
Apparently Grothendiek stated he didn't want any translations as long as he
lived. He died 5 years ago.

~~~
JadeNB
He didn't want his works republished at all; it wasn't an issue of
translation.

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jolmg
The README of the Github repo details their progress in the translation:

[https://github.com/ryankeleti/ega](https://github.com/ryankeleti/ega)

It seems they're done with EGA 0_I, and EGA I, but they're still working on
EGA 0_III, EGA 0_IV, EGA II, EGA III, EGA IV.

I wonder why there isn't an EGA 0_II mentioned...

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gwbas1c
What is EGA? (Enhanced Graphics Adapter? Extended Graphics Adapter?)

I clicked on the link assuming that there would be some kind of explanation,
but the page itself doesn't make much sense unless you already know a rather
significant amount of context.

~~~
wolfgke
> What is EGA?

Éléments de géométrie algébrique

[https://en.wikipedia.org/w/index.php?title=%C3%89l%C3%A9ment...](https://en.wikipedia.org/w/index.php?title=%C3%89l%C3%A9ments_de_g%C3%A9om%C3%A9trie_alg%C3%A9brique&oldid=937635310)

~~~
Koshkin
Thank god it’s not GA (not again).

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FisDugthop
I really like how the current top two comment threads need to be glued
together in order to get a coherent understanding of the timeline of this
work.

