Universally closed => quasi-compact

Today I learned a new basic fact on morphisms of schemes, namely the result mentioned in the title of this post. I started wondering about this question as I was thinking about separation conditions for algebraic stacks. Namely: it appears that the standard definition for a separated algebraic stack is one whose diagonal is proper, and I was wondering if we could get away with just requiring the diagonal to be universally closed and separated. It turns out we can due to the result of the title. After trying to think about it for a bit I decided to look for it on the web, and I quickly found a mathoverflow question asking exactly whether universally closed implies quasi-compact for morphisms of schemes, as well as the proof provided by Bjorn Poonen!

Note that all posts on mathoverflow are under CC-BY-SA, which is (unfortunately) not compatible with GFDL which is the license that the stacks project is under. Moreover, they ask to link back to their site, see here; and actually I think they are really stretching the meaning of the license since I think no linking should be required (IANAL). Anyway, I asked Bjorn if he agreed to relicense his material, and he said “Yes, that’s fine”. This means I need not link to their site if I do not want to (I did anyway).

It seems that CC-BY-SA is winning over GFDL in some respects, so I may switch the stacks project over to it in the future (there are still not too many authors so it shouldn’t be difficult to do). If I do this then I imagine I am allowed to take any latex code submitted to Mathoverflow by mathematicians and add it to the stacks project as long as I make sure to attribute it to the author of the comment. But for the moment, contacting the author of the comment and asking for permission directly makes more sense. Of course this is a bit difficult to do since it often isn’t clear who the author is especially for some very prolific contributors on Mathoverflow such as BCnrd…

Anyway, on a completely different note: I finally figured out how to set up the Makefile so that I can run the latex compiles in parallel. You will know why this is a problem if you’ve ever tried to write such a Makefile. If not it probably makes sense to stop reading this now. It is really quite simple (and I’m sure it is an often used trick). Instead of running latex stem.tex you execute a bash script which

  1. creates a temporary directory using mktemp
  2. copies all aux files and temp.toc to the temporary directory
  3. creates symbolic links in the temporary directory to stem.tex and stem.bbl (and maybe some style files, etc)
  4. changes directory into the temporary directory
  5. runs latex stem.tex
  6. moves stem.dvi, stem.aux, stem.toc back to the main directory
  7. removes temporary directory

Anyway, using this I was able to cut overall compilation time in half. On the server at work the times were

  • make dvis -j1 takes 1m42s
  • make dvis -j2 takes 50s
  • make dvis -j3 takes 33s
  • make dvis -j4 takes 25s

Not too shabby.

10 thoughts on “Universally closed => quasi-compact

  1. We’re willing to talk about this — we don’t really want to get in the way of people using content from MO, we were mostly just following the defaults from the Stack Exchange software, and hoping that this would protect us against any (imaginary?) abusive use of the content.

    I’d encourage you to come over to meta.mathoverflow.net to talk about it!

    • Actually, I thought about it some more overnight. Firstly, I now think I was perhaps wrong in understanding the licensing situation on mathoverflow, which would make the situation worse. Namely, I thought that somehow each of the comments on their was owned by the respective author (as on slashdot for example), but that may not be the case. So asking permission from the author of a comment might not be good enough — I may have to ask the author to send me the snippet him/herself under GFDL. Secondly, what is it that feels weird about the attribution “requirements” mentioned on the mathoverflow page? It is that you feel like you are attributing mathematical results not to a person or a group of people, but to an entity called “mathoverflow.net” (whatever that is). What if mathoverflow.net gets bought by some company?

      What I want is to be able to pick material from mathoverflow and say: Look here is a clever little argument by Brian Conrad (random example). I do not want to have to link to the location. Sometimes I will only mention the author in the commit message in the log of the stacks project since that is really the definite log of who contributes what to the stacks project, and not in the actual pdfs of the stacks project itself.

      I think the current situation (with incompatible licenses) is actually preferable, since it will force me to do the correct thing, and each time approach the author of the comment him/herself.

      Mathoverflow is just an example. There are other questions of copyright in mathematics that I am not confident about. Namely, most of what I have written so far in the stacks project I have written from memory (believe it or not). Of course it is allowed and encouraged to take the material from mathematical papers and reformulate it (and I think this should also apply to material from mathoverflow). Many research papers consist largely in rewriting existing material for example (with vague references and often incorrect attributions). Still it seems that somewhere there is a line that should not be crossed. It seems wrong to take the source of an arXiv paper and copy paste it into the stacks project — but is having the paper open in one window and retyping it in another OK? Is it OK if you change the mathematical setting slightly? How about correcting serious errors in a paper (by editing the latex source) and reposting on the arxiv? Wouldn’t it be beneficial to mathematics to allow this?

  2. The discussion on meta.mathoverflow is at http://meta.mathoverflow.net/discussion/503/cc-licensing-vs-gfdl .

    Since MO consists entirely of “little arguments”, it’s hard to imagine a legitimate example of use of the material which couldn’t be defended as fair use. My assumption was that the only situation where you’d really have to worry about the license is if you wanted to republish large chunks of MO verbatim.

    The copyright is retained by the person who posted the material, so you can do whatever you want with the material if you get permission from the author.

    The attribution requirements were meant to get people to attribute the material to the authors, not to MO. They were lifted from Stack Overflow’s requirements (http://blog.stackoverflow.com/2009/06/attribution-required/) on the assumption that the guys at SO have thought this out more than we had. I don’t know to what extent those requirements are legally binding, but I would have no objection to changing them to whatever is closest the the accepted standards of using mathematical material.

    • Well, I am not going to take any vague assurances like that for granted. The requirements on mathoverflow clearly state that you have to attribute to mathoverflow.net. I do not think it is necessarily the case that the copyright remains with the author once they upload their comment into mathoverflow (are you sure?). But if the author has the original latex source in a file somewhere, then I think it is their right to license it under GFDL and submit it to the stacks project.

      Of course this kind of thing always leads to long discussions and flame wars, and in some cases to really annoying situations. I believe I understand well enough what it means to use GFDL (without invariant sections; and I am aware that you can criticize GFDL). I am not as clear on what it means to use CC-BY-SA in a large scale setting. I think you guys should rethink this stuff, talk to a laywer, figure out exactly what is true and what is not and change the wording on the “attributions required” page linked to in the post (if it is not exactly right), but of course it is up to you.

      Since to me it is very important that the stacks project never gets in a difficult situation because of this kind of thing I am going to play it safe, and always directly email the author of the comment, and ask the author to submit it to the stacks project directly. I hope you agree that this is “playing it safe”.

      • IANAL, but I believe you retain copyright to anything you write unless you explicitly transfer it to another entity.

        Also, I believe it is better practice to link to the mathoverflow answer for your clever argument than to use the more common practice of citing “private communication” or “unpublished notes” or even “proof of lemma x.y.zz.y in this 100 page paper”.

        • What about the fact that others are allowed to edit what your post on mathoverflow? It says this literally here., and it says something about “releasing” under CC-BY-SA?!? I think the interesting question for the mathoverflow people to figure out is who holds the copyright; I mean which legal entity holds the copyright (it may not be a person or group of people). How does that work?

          Why do you think it is better to link to mathoverflow than a published paper? Nothing on mathoverflow is refereed, anybody can hide behind a name (in principle), and people can make mistakes there (as well as in papers of course). Also, there may be a misunderstanding between what is asked and what is answered, etc. I do not think it is better. In the particular case of the result mentioned in the post I would be very happy if somebody found a reference in the literature (which may very well exist), since it would make me feel a little more sure that the result is correct (even though I went through Bjorn’s argument with a pretty fine comb), and moreover, there would be a context in which the result appeared which would be interesting.

          Another objection to referencing mathoverflow is that mathoverflow.net may die (I mean the website). The mathematical content may still be there (in the form of a data dump or whatever, and maybe re-spawned somehow somewhere else). I am really not that happy with having to attribute a result to a website. I’d much rather give credit to a person, or a group of people (provided they actually did something). Similarly, for a reference, I would much rather reference actual content (e.g. a precise lemma, proposition, theorem) of a paper, book, or collaborative work, than a web location. (Of course the stacks project does not have outside references so this does not apply to the stacks project.)

          • It’s not that I believe that linking to mathoverflow is better in general than citing a published paper, it’s that for a short argument, it’s easier for a reader to look at mathoverflow to see what the argument is and why/whether it works than to dig up a paper than maybe isn’t online or in the library, or is behind a paywall.

            Yes, people (with enough reputation) can edit your posts – that’s what you agree to when you use the site. But that doesn’t mean you don’t have copyright on what you write, it just means that you’re publishing it with a particular set of conditions. CC licenses similarly don’t mean you forfeit your copyright, they just say that you as copyright holder agree in advance to let other people do certain things with your work. The edit history on mathoverflow is entirely transparent – you know whether a post has been edited and by whom, and if you click you can see a(n attributed) list of all changes made to the original post. In practice, the vast majority of edits seem to be editing tags and fixing typos and faulty LaTeX and minor mathematical errors.

            I agree, websites can die, but so can journals. Or they can be discarded or shipped to an offsite storage facility because the university libraries are running out of space (the Columbia libraries, for example, store a lot of their collections in an offsite facility in New Jersey). Or they can be obscure or expensive enough that a reader’s library doesn’t subscribe to them. I’m not denying that digital preservation of data is a serious problem, but it’s a whole separate discussion, and the same arguments apply to the stacks project being a web-only project.

            The citation style requested by MO clearly attributes mathematical content to the authors, so I’m not sure what the problem is. The cc-by-sa license says that creators have the right to set attribution styles. Is your argument that MO doesn’t hold the copyrights and therefore the individual authors should be the ones linking to the cc-by-sa website? I would argue that contributors agree to have their contributions be released under cc-by-sa with the given attribution style when they use the site.

            I guess my question is, what would you have done differently if Bjorn had e-mailed you the answer in question? If it were a paper, you would probably have acknowledged his contribution by saying something like “B. Poonen gave me the following argument” and citing it to “private communication”. I’m not sure why that’s different from saying “B. Poonen gave the following argument on mathoverflow”. And in either case, if you wanted to copy the argument verbatim, you would need Bjorn’s permission (since AFAIK you have copyright on everything you write, including e-mails).

          • Review: (1) I currently cannot use material from mathoverflow because the licenses are incompatible, hence I have to ask the author each time. (2) What I do not like is having to put in the link. (3) If I ask the author to submit their content to the stacks project under GFDL I do not have to put in the link. Simple right?

            I think you are making some good points on the attribution question. Thanks! I guess my main annoyance is with having to put in a link. I still do not think the situation is quite as simple as you make it out to be with the rights to the comments on mathoverflow.

            References: I also agree with some of what you said about journals, etc. It still seems strange to reference a web location rather than a particular mathematical result which is published somewhere on the web. When you reference the stacks project, you should say something like Lemma Tag 0234 from the stacks project. The stacks project may be moved, or the lemma may move in the stacks project, but the reference still works. Something similar is true for references to Russian papers — and then looking at the English translations. But I guess you are going to argue that the link to a comment on mathoverflow has an identifying number in it. Hmm…

            The answer to you final question is: There would not be a link.

          • [This is meant as a reply to Johan’s post below, but there isn’t a reply link on that one]

            Would you be happier if rather than having to link to the original post and the author’s profile page, you only had to provide the post ID of the post and the user ID of the author? In other words, instead of having to say “http://mathoverflow.net/questions/12345” you could say “post 12345 on mathoverflow.net”.

            It seems reasonable to require at least enough information to find the original post and the original author. Since question titles and user names are not unique, the post number and user ID are the only thing you can use. It’s true that the post number is enough to recover the author, but I think including some author information is pretty standard.

            Again, I’m pretty sure that these requirements would only apply to a situation where (1) you’re copying something verbatim, (2) it’s large enough that it’s not fair use, and (3) you haven’t gotten special permission from the author.

          • Rebecca’s comments made me look at CC-BY-SA more carefully, and I discovered at the bottom a link that brings you to the actual legal text. Of course it is basically impossible to understand. But I found the following snippet. I quote (with omissions)

            If You Distribute …any Adaptations or Collections, You must, unless …, keep intact all copyright notices for the Work and provide … (i) the name of the Original Author … for attribution… (ii) the title of the Work if supplied; (iii) to the extent reasonably practicable, the URI, if any, that Licensor specifies to be associated with the Work, unless such URI does not refer to the copyright notice or licensing information for the Work; and

            It seems to me that the URI of a mathoverflow question does not refer to the copyright notice or licensing information for the Work. So it seems to me that (if I were using CC-BY-SA and I copied material from mathoverflow) I don’t have to put in a link to the exact spot in mathoverflow where the material appeared. Right? So that means you guys do not have to worry about it at all, since the license text itself takes care of it. It does make me feel a bit vindicated (if I understood the passage correctly), that the formulation on the mathoverflow page dealing with attribution is stretching what is required. Maybe the formulation could be changed into “we ask that you insert a link to” and on top of that you can require a link to some page on mathoverflow discussion the licensing. Of course I may very well be wrong again.

            In response to the comment of Anton: Thanks for trying to figure out what would work! As discussed above, this is currently not relevant. Still, here are some comments: Yes, I am talking about copying latex code verbatim (I think the fact that I then edit it myself is irrelevant — unless I change it beyond recognition). Yes, I agree that mentioning the author is good practice (I still think the concept of who is the author on mathoverflow is a bit fluid). Finally, the “citing” suggestion on the mathoverflow attribution page seems reasonable, since I finally figured out (see above) that the number contained in the link is future proof in the sense that it somehow continues to work even if mathoverflow.net dies.

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