@robinhoode And here's another one in English: numdam.org/item?id=PMIHES_1966__29__95_0 If you click on G.'s name there, you get access to about 50 articles by him (most in French, of course).
And SGA is here. That should be enough for the moment, I think. Come again in 10 years :)
@robinhoode You can get used to it pretty quickly I think. But I mostly read articles in languages I master pretty well, so I can't tell how hard it really is. Here's a relevant MO thread on this.
One would think a visually oriented person would develop a better sense of when the prose he produces just doesn't look like other English prose locally.
@t.b. Hello again. Sorry for leaving abruptly yesterday. I tried again yesterday to prove the assertion, but in vain. Then it came to me that a subgroup of a topological group needs not be normal, but needs for the homogeneous space to be a quotient group. Therefore, even though every homogeneous space apparently satisfies the two axioms listed, they are not always groups, right?
@Srivatsan I understand. Someone will certainly patiently explain the purpose of counterexamples. It is quite an achievement to get as far as Fubini's theorem in order to learn this lesson... I tried to leave an explanatory remark.
@awllower Wait: let's not talk about topologies, yet. You can only be sure that a subgroup is normal if the group is abelian. In non-abelian groups you tend to have subgroups that aren't normal. No: a homogeneous space X does not satisfy the two axioms because multiplication is not defined between two elements of X but rather you have a transitive operation G x X -> X
@awllower: I haven't really thought about this in a long time, so I can't give you pertinent hints, but I'm pretty sure I did it the verification, so don't give up! The idea is that you can find right and left neutral elements of each element and corresponding left and right inverses. Combining these and using associativity, you can identify them the way they should be. If you really don't manage to do it, why don't you ask on the main site?
I remember that it was fiddly. The reason it hasn't caught on is precisely this: you have to work a bit in order to get to the point where others start with their definition of a group. Meanwhile, you can just as well work with the usual definition of a group and read Weil's book this way. You won't miss anything important by doing so.
@t.b. Indeed, I see what you mean, and I intended to do this before, but then I somehow entered a mode that is close to skimming the book, the least thing I would like to do, especially to the book by Weil.
@awllower Well, I hope you will manage to do it. I don't think that Weil ever explicitly uses these axioms. At the latest when he introduces topological groups about a page later he takes all the standard facts about groups you know for granted, so there is no real risk of missing much that I can see from afar. I wish you many pleasant and illuminating hours with this wonderful book!
@Srivatsan Yes, it's my first second language. About half my family speaks French. I grew up in Bern which is pretty close to the border between the French speaking part and the German speaking part of Switzerland.
@tb I cannot read any technical work in my first language, namely Tamil. Partly because none of the advanced material is translated into it, partly because of my english education.
Do(did) you face something similar when reading French books?
@Ethan I don't think you need that much for modern texts. However, the books by Bourbaki or earlier works need quite a bit of sophistication. Here's a MO thread on this.
@Srivatsan No there's nothing really comparable here. Both French and German have technical literature at every level (though since a few decades German isn't used that often for research papers anymore). I learned the technical words in French quite quickly, I sort of assimilated them as I did it with the English terms. There are some differences but not that many.
@Ethan By the way, there's no single language called "Indian". The closest to that description is Hindi, the national language. But I can't really read, write or speak it fluently... =)
@Ethan I made the experience (sort of) when I was digging in the Romanian literature for some technical results I needed for my work. I don't really know a word of Romanian but reading it was rather easy. Of course, it's a Latin language, so a lot is self-explanatory. I imagine that a similar effect works when reading French math with a good English background: many words are similar and the few clauses needed are quickly absorbed.
Yes I agree. I created a link bar with direct short cuts to the tabs I need, so I hope I can get used to that quickly.
One thing I sorely miss (in the old and in the new interface) is that it isn't indicated who asked the question I answered. That would help a lot in locating what I'm looking for.
@JM It's a terribly bad idea. I'm using the script... Anyway, Arturo's request for un-CW-fication is the only implemented one I can think of at the moment.
@Ethan German and English are certainly very close. But French and English aren't that far away from each other either. At least I could rely on my French vocabulary to sound awfully sophisticated in my early English classes.
@JM I wasn't around when this happened, but I think the fact that several sites now have TeX is also due to MSE.
@Srivatsan The formulae thing? As I said, I'm too lazy to remember unicode for ligatures... remembering accents, graves and umlauts is tough enough already. ;)
In one paper I wrote I had a big fight with the typesetter because I insisted that sheafification should be written with only one fi ligature (the second one) while the first one shouldn't have a ligature. I lost the fight, obviously.
@JM In French there is the even more complicated equivalent of "to pass to the associated sheaf". But French people are more reluctant with introducing new words. I distinctly remember hearing a long interview on the radio with Laurent Schwartz where he goes at great length about the reluctance he had to overcome before introducing and using the word "convolver"
In the Swiss dialect we are quite liberal with using all kinds of words. We use a lot of French and English imported words (sometimes distorted byond recognition). That's one reason why I have a bit of difficulty reading German advanced math texts - I don't know the words they're using. Sometimes I have to translate them into English in order to understand what they could possibly mean...
(But I think I told you that already on another occasion :))
Actually, there are a few French words imported in German, too: for example "Schorle" (a beverage: wine or apple juice mixed with mineral water) - it's derived from the way of saying "cheers" that was common among French soldiers during the occupation in one German/French war: toujours l'amour, l'amour toujours. It became "Schorlemorle" and then later simply "Schorle".
@JM I suspect interference with MarkDown, interestingly enough, underscore works... I don't quite understand what is going on there, you can't use neither LaTeX nor markdown nor html, but typesetting seems to be equivalent to using mathrm
