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    • CommentAuthorEmerton
    • CommentTimeFeb 4th 2010 edited

    This question about learning the theory of Shimura varieties was closed, on the grounds that it was an exact duplicate of a question about learning the theory of Shimura curves">question about learning the theory of Shimura curves.

    Shimura curves are very special (and relatively simple, being curves) kinds of Shimura varities, and, in my view, to answer the question on Shimura varieties by referring to a discussion of Shimura curves is akin to answering a question about the arithmetic geomery of abelian varieties by referring to Silverman's book. I don't think it makes sense as an answer; the questioner simply would not find anything substantantive about general abelian varieties in Silverman, and even less will norondion find anything substantive about the problem of learning the general theory of Shimura varieties in the answers about Shimura curves.

    What's more, the theory of Shimura varieties is notoriously difficult to learn, so having a discussion of possible approaches and references on MO would be a valuable resource, not just for norondion, but I imagine for many others as well.

    If anyone with voting rights agrees with me, they could join me in voting to reopen.

    Of course, I would also be happy to hear the reasoning of those who voted to close.

    That question seemed pretty close to the one about Shimura curves, and as posed is a pretty marginal question. So it seemed safe to vote to close it. Maybe that wasn't a good enough reason.

    Since I can tell you're just dying to give an answer to it, I've voted to reopen.

    I didn't vote to close, and I don't know anything about Shimura anything. My guess is that the main reason people voted to close is that it looks like a ripoff one-line version of the very thoughtful Shimura curves question, and people wanted to discourage "how do I learn about X" questions if it doesn't look like the author put any effort in.

    • CommentAuthorEmerton
    • CommentTimeFeb 4th 2010 edited

    Dear Charles and Anton,

    Thanks for responding. I can understand that people thought this was a marginal question, but that is not the reason given for closing. And my belief is that to describe it as an exact duplicate is just wrong.

    More generally, my impression is that people are a little too ready to close/criticise (and while I realize that these are not the same thing, they are not completely unrelated things either) questions. If someone else wants to procrastinate by answering a question you don't like personally, I don't see the harm in letting them do that (speaking purely hypothetically of course; "dying to answer it" is a bit strong, but as I commented, I'd be happy to give it a go in an idle moment). Anton, I think you already know that I am far to the left on this issue (if I can describe it that way).


    @Emerton: I'm not defending closing the question as a duplicate, but I think I'd be willing to defend closing the question. If somebody posts a question whose entire body is "how do I learn about X", it's really annoying, no matter how interesting X is. At the very least, I'd like some explanation of why just googling for X doesn't work.

    The Shimura curves question beautifully motivates why the question is being asked and even provides the background the asker is coming from. It sounds like you would have no trouble motivating why the Shimura varieties question is being asked (or why it should be asked), so I invite you to edit the question to say something about why the theory of Shimura varieties is difficult to learn, or at least that it is difficult to learn.

    • CommentAuthorEmerton
    • CommentTimeFeb 4th 2010

    Dear Anton,

    I can see the merit of your position (on this matter and more generally), even if I don't always agree with it. As to editing the question, it's a nice suggestion (though less fun than answering!).

    Best wishes,


    @Emerton: as of this moment, the question is open again, which is probably as it should be.

    As I said, I think I just missed the word "varieties" in the statement of the question the first time through. I did not vote to close, but my comment may have encouraged others to do so, so that was a bit of a mistake on my part, I think.

    I do think that there is something to the "closers'" position, though. "Tell me about broad, difficult topic X" is an almost platonically ideal bad MO question of a certain type. It gives almost nothing and asks for a lot. It is impossible to give an answer to such a question which is in any way tailored to the needs of the questioner, so at best it is more like an excuse/invitation for someone to riff on the given topic. [By the way, I think the question is sufficiently vague so that a reply which is given entirely in terms of Shimura curves _could_ be what the questioner wants to hear, just as if someone asked me "What is an abelian variety?" my initial response would probably be mostly in terms of elliptic curves: if someone really knew elliptic curves well, they probably would be able to understand the definition of an abelian variety well enough to ask a more specific/motivated question.]

    The flip side of course is that an excuse/invitation to riff can lead to some nice answers! I have myself given at least popular answers to vaguely worded questions, and in this case I am distinctly looking forward to your answer. Please riff away...
    • CommentAuthorEmerton
    • CommentTimeFeb 4th 2010

    Dear Pete,

    I agree that the question was about as short and unmotivated as it could be. On the other hand, I'm inclined to give the questioner the benefit of the doubt in these situations, and to answer/riff if it seems like fun to do so. (And this question should be fun, when I get a chance!)


    I was the first person to throw the stone, so let me explain my reason.

    When I noticed that the question is a bit different from the Shimura curve question, it wasn't clear what is the level on which to respond to it. It could be that the OP has already looked into Wikipedia article and the Shimura curve question — it could be that OP has just started to learn about Shimura varieties; or it could be that s/he isn't really looking for a long and detailed explanation but rather for some particular aspect.

    For example, norondion has already asked some more technical questions like Why is one interested in the mod p reduction of modular curves and Shimura varieties?.

    Since this wasn't clear from the question, I decided that the ideal situation would be for OP to clarify a bit his/her background and what kind of answer is expected. To that end, I voted to close but left the comment asking to clarify it — my goal wasn't to leave it closed forever, but rather to see it changed. Whatever clarification the OP would make was going for me to be sufficient to reopen it.

    If I knew you would be willing to respond immediately, the calculation would be a bit different: having a good answer to the question would be guaranteed irrespectively of the question's merits; in that case I wouldn't be closing it.

    Apologies if that looked harsh; I've been on the other side when I was asked by Scott and Anton to stop some of my questions that asked to review a particular topic and typically provided a paragraph or two of background. From that experience I had an impression that MO's accepted policy is to send questions that ask to write a review article to nLab by default.

    • CommentAuthorEmerton
    • CommentTimeFeb 5th 2010

    Dear Ilya,

    Thanks for responding. I appreciate your motivations. As I wrote above, I think I am fairly extreme in my reluctance to close questions, and in this case, as you know, I was also concerned about the justification for closing (duplication) as much as the closing itself. I agree that it wouldn't hurt if norondion was to give a little more detail in the question (e.g. at what technical level they want the answer to be).


    I think that the "duplicate" tag is unwarranted, but mainly because the two questions are in completely different leagues.

    I would strongly recommend not answering the later question (the one originally closed as a duplicate). I am ambivalent as to whether or not it should be closed-awaiting-refurbishment or left open in the hope that it gets tidied up a little.

    I am sure that someone (Emerton, presumably) could give a fantastic answer explaining how best to learn about Shimura curves and the distinction to Shimura varieties. I'm sure that anyone who stumbled on the question would learn an immense amount from such an answer. It is clear that such an explanation would greatly benefit the mathematical community.

    However, such an answer is not a suitable answer for this question. My issue with this question (and with so many like it) is that it is impossible to judge what would be a suitable answer for this question. Someone could spend ages crafting a fantastic answer that would completely go over the head of the original questioner. MO is for asking questions and getting answers to those questions. It is a place for dialogues, not for monologues.

    I can understand the desire to nonetheless leave helpful answers so that anyone stumbling over them later can benefit. This was the argument voiced after Tim Gowers left a great answer to a similar-standard question on functions in probability. But whilst MO does a half-decent job at creating a repository of knowledge, it's not the best place for such. If someone really has a desire to write a great expository article on the difference between Shimura varieties and Shimura curves, please do so on a wiki somewhere and then link to it from MO.

    I'm not saying this just to drum up more articles on the nLab. But expository material belongs somewhere more accessible than in the depths of the MO database. Keep answers focussed on their questions on MO and when the urge comes to write something extensive, put it somewhere more appropriate.

    Back in the early days of MO (where's that zimmer frame gone?), Anton and I had quite a debate about what was and was not appropriate on MO. He was trying to persuade me not to twist MO to my own nefarious purposes. He might be interested to know that I now agree with him. The strengths of MO lie in the interaction between asker and answerer. If an answer does not engage with the asker, then it's a Bad Answer, no matter how fantastic the rest of us think it is.


    I completely agree with Andrew, and he's stated the objection much better than I could have. It is exactly the reason Ilya voted to close. Linking to a (freshly written) nLab page and closing the question is the most appealing option to me, but I didn't realize that until Andrew said it. If I could vote to close as a regular user (rather than as a moderator), I'd do it. (Sorry, this is somehow coming off more contentious than I meant ... I just wanted to express my agreement with Andrew and with Ilya's initial reasoning)

    • CommentAuthorEmerton
    • CommentTimeFeb 5th 2010

    Dear Andrew and Anton,

    Thank you both for explaining your perspective.

    Best wishes,


    To be honest, if someone like Emerton posted a question and then posted an answer to it just so people could read about it, I wouldn't mind.

    @Harry: yes, but he would have surely posted a better question! I think the point here is we try to encourage good questions. For example, I can google "Shimura variety" and find right away a wiki page, a nice-looking note by Milne, and a video lecture by Falting! It is not clear what the OP has tried before he asked and why those materials do not work for him.

    Oh sure, I'm just saying that I'm not against having a sort of "lecture on MO" every once in a while. I think it would be pretty interesting.
    Right, how could anyone still have questions about Shimura varieties after reading a note, looking through a wiki and watching a video? I guess some people are just unteachable. :)

    This time I agree with EVERYBODY, even when you don't agree with each other. (Seriously.)
    Hah! You agree with me, but my comment was only tangentially related to the topic at hand.

    @Pete: I do not mean one can learn things like that via Google. If anything, the fact that Milne wrote a note and Falting gave a lecture indicates that this is hard stuff (: My point was there seems to be resource around, and I would appreciate if the OP posted some of those so we have a starting point.


    To be honest, if someone like Emerton posted a question and then posted an answer to it just so people could read about it, I wouldn't mind.

    I think that on SO, this is actually encouraged. But as Hailong says, he'd probably do a better job of asking the question. I can easily see a reason for this: if one finds that people frequently misunderstand something, then one could post a question and its answer. Then everyone would read the question, realise that they misunderstand it, and be enlightened at the same time. There are probably other situations where this would also be appropriate.

    Then perhaps if Emerton really wanted to answer the question, he could be encouraged to re-ask it himself?

    By all means, let Emerton answer the question and edit it to his liking (or not edit at all).

    Note also that we are discussing this question for two days without the OP (his userpage says that asking the question was the last thing he was seeing doing). I think if he was here to make some comments we would either quickly reopened the question or agreed that it's not salvageable.


    Minor point: if Emerton were inclined to post an answer to this question, I really would recommend that he ask his own question on it (and then answer straight away) rather than editing this question.