Style[ edit ] The material has a reputation of being hard to read for a number of reasons. The style is very abstract and makes heavy use of category theory. Moreover, an attempt was made to achieve maximally general statements, while assuming that the reader is aware of the motivations and concrete examples. They can still be found in large math libraries, but distribution was limited.
|Published (Last):||5 April 2011|
|PDF File Size:||5.56 Mb|
|ePub File Size:||20.68 Mb|
|Price:||Free* [*Free Regsitration Required]|
That is so true. I needed some facts concerning differential operators for my PhD thesis. And there it all was: very clearly and thoroughly stated.
I was ashamed I let the immensity of the work scare me away before. You only know what you are looking for once you are actually looking for it.
It is an incredible resource, in terms of its completeness, its level of detail, its generality, its open discussion of its goals, assumptions, and choices of proof, and for many other reasons. And it has the mesmerizing quality of reading EGA, or of a well cross-referenced encyclopedia: you turn to it just to look up one small fact, which leads to another, and another, It is evidently a mathematical masterpiece of a certain kind, but I would never recommend it to a student to study.
But one thing to remember is that many very clever people have pored over the details of EGA and SGA for many years now, and it so it is going to be hard for anyone to find interesting new results that can be obtained just by applying the ideas from these sources alone as important as those ideas are. Even if you want to make progress in a very general, abstract setting, you will need ideas to come from somewhere, motivated perhaps by some new phenomenon you observe in geometry, or number theory, or arithmetic, or ….
By themselves, they are not likely for most people to provide the inspiration for new results. 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.
But you will likely have to find your inspiration elsewhere. I think it is worth thinking about two of the most significant recent theorems in algebraic geometry: the deformation invariance of plurigenera for varieties of general type, proved by Siu, and the finite generation of the canoncial ring for varieties of general type, proved by Birkar, Cascini, Hacon, and McKernan, and independently by Siu.
Certainly Griffiths and Harris for the very basics, but then The methods of BCHM are techniques of projective and birational geometry. 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. An aside: there is much more to EGA than just handling non-Noetherian schemes, but the spectre of non-Noetherian situations seems to loom a little large over this discussion.
More generally still, this is probably a good summary for my case against spending time reading EGA.
Donate to arXiv
Life[ edit ] Family and childhood[ edit ] Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro also known as Alexander Tanaroff , had Hasidic Jewish roots and had been imprisoned in Russia before moving to Germany in , while his mother, Johanna "Hanka" Grothendieck, came from a Protestant family in Hamburg and worked as a journalist. Both had broken away from their early backgrounds in their teens. They left Grothendieck in the care of Wilhelm Heydorn, a Lutheran pastor and teacher   in Hamburg.
Subscribe to RSS