Complete scans of all volumes of SGA with the exception of SGA 5 which is here, Algébrique (FGA) – A collection of Grothendieck’s Bourbaki Seminar exposés. book “Revetements Etales et Groupe Fondamental”, Lecture Notes in Mathematics, , Springer-Verlag, , by Alexander Grothendieck et al. In French. Préfaisceaux, par A. Grothendieck et J.-L. Verdier: (original, réédition); Topologies et faisceaux, par J.-L. Verdier: (original, réédition); Fonctorialité des.
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Their writing is roughly synonymous with the founding of modern algebraic geometry as a field. Email Required, but never shown. I had a great time in a “seminar of pain” with a number of other people who were also already reasonably happy with Hartshorne and more. The material has a reputation of being hard to read for a number of reasons. Grothendieck outlined what grothendieckk meant to be in chapters V-VII, at least, and some handwritten prenotes existed for a small part of those.
Silverman Fulton’s intersection theory. And the more you visit, the more pleasant it is to see things done elegantly and in full as humanly and humanely possible generality. When you are starting to learn algebraic geometry you have to cover a lot of material.
[math/] Rev\^etements \’etales et groupe fondamental (SGA 1)
A careful reading of Hartshorne, especially the last two chapters, would be a good preparation for entering the research literature in this subject, I think. Unless you have a really special interest, you shouldn’t.
I do think the project of reading EGA would be of great value to an aspiring algebraic geometer; but there are lots of other projects with this property, and I grothendiwck think reading EGA is indispensable in a way these other projects are not. You need to consider non-Noetherian schemes when doing some natural constructions in arithmetic geometry. You can find a handful of abortive attempts at translating EGA around the internet. Hartshorne’s book is good, but at times he considers only schemes over algebraically closed fields, where he could be more general.
At the time I write this, there are a number of wise words already written here, so I’ll add just incremental thoughts. Hartshorne, Some complex-point-of-view book e. But this is less true than a wga ago. I suppose I end up giving a rather mushy answer; if reading EGA appeals to you, then you will probably be drawn to the kind of problems where it’s essential that you’ve read EGA. As a first step, the entire work was scanned and made available on-line see the links section below by Frank Calegari, Jim Borger and William Stein.
On the other hand, when you are trying to prove your theorems, you might well find techincal tools in them which are very helpful, so it is useful to have some sense of what is in them and what sort of tools they provide.
The seminar notes were eventually published in twelve volumes, all except sgaa in the Springer Lecture Notes in Mathematics series.
I have examined all these books for learning Ag such as Hartshorne’s book but in eventually I learned almost nothing from these books then I had to try other books which are written in the field of algebraic geometry, but unfortunately grohhendieck books also had the same result as Hartshorne’s book. That is so true.
Mathematics > Algebraic Geometry
The French language may be a barrier for some, but one doesn’t have to “learn French” to learn enough to understand EGA. Some will read them later for “pleasure”, like reading the classics. If not, then maybe not. Thus it seems worthwhile to mention that, while non-Noetherian schemes arise naturally in certain contexts as Kevin Buzzard noted in a comment on David Levahi’s answerI think these contexts are pretty uncommon unless one is doing a certain style of arithmetic geometry.
The methods of BCHM are techniques of projective and birational geometry. For reading EGA the most precious and rich sources not only in the context of algebraic geometry but throughout all of mathematics first you need to learn a little French language. Here is a list of what you must cover: This site is running on Instiki 0. He told me not to be absurd, that I should just learn techniques as I needed them for problems.
Then you revisit the same topics and, with your new and better perspective, you appreciate more of it. That’s proof enough for me.
So my recommendation is: In response to a similar question asked on Terry Tao’s blog, I posted the following advice: In the late 60’s and early 70’s, the original seminar notes were comprehensively revised grothejdieck rewritten to take into account later developments. You want to be able to do exercises, then answer questions, then ask questions, then do something new.