I'm just trying to add the abstract algebra tag to this old question I just bountied and the same user keeps rejecting it: Closed subscheme of a projective scheme determined by homogeneous ideals

Can someone help me out or explain to me why the abstract algebra tag is inappropriate for a question about graded rings?

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    $\begingroup$ Link to the edit reviews: here, here. $\endgroup$ – Arctic Char Oct 23 '19 at 2:57
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    $\begingroup$ FWIW, I disagree with the reviewers and to be very honest, cannot understand their line of reasoning. I certainly would have approved the edit if I were reviewing. I agree with Xander however that you shouldn't re-suggest an edit after it's already been rejected. $\endgroup$ – YiFan Oct 23 '19 at 22:35

Some comments:

  1. Algebraic geometry is related to abstract algebra, just as differential geometry is related to calculus.

  2. You want to add a tag to attract people interested in algebraic geometry, can the "abstract algebra" tag work? Is there any user who (i) is interested in AG, but (ii) watches ONLY the "abstract algebra" tag but not the AG tag?

  3. The question you linked cannot be understood by people having only a course in abstract algebra. There won't be any user who is interested only in abstract algebra and happens to know the answer to the linked question.

  4. Tags are also used in a way to block questions. For example, there might be some users who are interested in AG, but are tired of proving the first isomorphism theorem of groups again and again. They could hide questions with the abstract algebra tag and watch only the AG tags. If a question is tagged with both tags, these users cannot see it.

There are cases where adding a more general tag works. For example, this was asked two months ago and was tagged only with "differential topology". The question went unnoticed until recently, when someone added the "differential geometry" tag. This immediately attracted more users and the comment below the question more or less answered the question.

Questions went unnoticed if only rare tags are used. Users might still watch the tags, but they do not visit frequently since there aren't many new questions (For example, I am interested in differential geometry in general, but won't visit (e.g.) the mean curvature flow tag frequently). In this situation adding a more general tag would work.

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  • $\begingroup$ i think this is fair -- maybe the rule is go to the most general tag that a knowledgeable person would reliably check $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 4:14
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    $\begingroup$ A couple of pedantic thoughts: (1) If someone has proved the FIT for groups over and over again on this site, then they shouldn't be proving it again. Rather, they should be flagging duplicate questions when they come up. This is a good reason to have tag experts, and to use the appropriate tags (e.g. not too general, not too specific). $\endgroup$ – Xander Henderson Oct 23 '19 at 12:36
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    $\begingroup$ (2) I would argue that differential-topology is neither more specific nor more general than differential-geometry, so I am not sure that this is a great example of a post getting more attention when a more general tag is added. Rather, it is a good example of how the correct tagging can help a post get attention. $\endgroup$ – Xander Henderson Oct 23 '19 at 12:37
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    $\begingroup$ @XanderHenderson For the second point, the relationship is that people working in differential geometry has to know differential topology (to some extent) but not vice versa, and it seems that the differential geometry tag is the "umbrella" tag for all related fields. So for example, lots of questions in the DG tags indeed do not have "geometry" in it. But yeah, it is a correct tag, in the sense that it works... $\endgroup$ – Arctic Char Oct 23 '19 at 13:39
  • $\begingroup$ @ArcticChar You might be surprised. I know a number of physicists who are pretty competent differential geometers, but who haven't the slightest clue about what an "open set" is, let alone a topological or differential manifold. This is, perhaps, similar to an undergraduate who has taken real analysis, but not topology. $\endgroup$ – Xander Henderson Oct 23 '19 at 16:19
  • $\begingroup$ however i dont really agree with your first point. and even granting that point, if someone asked a DG question which is almost exclusively an exercise in calculus (carrying the analogy over to the question i bountied), i cannot really understand an objection to the calculus tag. $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 23:22
  • $\begingroup$ @XanderHenderson To be honest, I won't call someone a differential geometer, if they do not even know the definition of a differentiable manifolds. $\endgroup$ – Arctic Char Oct 24 '19 at 2:53
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    $\begingroup$ @dessind'efantterrible The question you bountied is far from being "exclusively an exercise in abstract algebra". $\endgroup$ – Arctic Char Oct 24 '19 at 2:54
  • $\begingroup$ @ArcticChar i said almost. its essentially just asking to find a homogenous ideal in a graded ring S that localizes to some prescribed ideals is some localizations of S. it could be asked without any mention of schemes. $\endgroup$ – dessin d'enfant terrible Oct 24 '19 at 5:57
  • $\begingroup$ @dessind'efantterrible If the question is framed completely in terms of graded rings and localization, then the "commutative-algebra" tag is appropriate (I didn't read Ravi Vakil's notes, I assume they are also working on commutative rings), and I still don't think "abstract-algebra" is useful. $\endgroup$ – Arctic Char Oct 24 '19 at 6:22
  • $\begingroup$ @ArcticChar One doesn't have to be a differential geometer to ask a question about differential geometry. ;) $\endgroup$ – Xander Henderson Oct 24 '19 at 12:24

The tag is a very general tag which is generally relevant for questions regarding groups, rings, fields, modules, and vector spaces. These kinds of questions tend to pop up in advanced undergraduate or elementary graduate level courses. The question being considered here is about algebraic geometry which is a much more specialized field. The question was appropriately tagged with .

For comparison, this is somewhat analogous to the distinction between the tag and the tag. Questions involving the Hausdorff measure are likely questions about analysis, but the Hausdorff measure is a more specific tag, and questions about the Hausdorff measure may not be relevant to the folk who follow the analysis tag.

In short, I think that the reviewers made the right decision.

As an aside, suggesting an edit after it has already been rejected is inappropriate. In the future, if you feel that a review is mistaken, please raise the issue on meta or in chat (either Tagging or CRUDE might be a good place to look for help).

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  • $\begingroup$ so just to be clear youd object to the analysis tag on a question about hausdorff measure? $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:10
  • $\begingroup$ imo the purpose of tags is to increase visibility of the question to people who may know the answer. e.g. you surely agree that just tagging something as hausdorff measure torpedoes its visibility $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:13
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    $\begingroup$ if the only purpose of tags were to indicate the topic then there would in fact be no need for the algebraic geometry tag either, since "schemes" already more narrowly and completely defines the subject of the question $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:16
  • $\begingroup$ The analogy might not be appropriate: while abstract algebra is a good tag, there are discussions about the analysis tag, which suggests that it is in itself too general: here. $\endgroup$ – Arctic Char Oct 23 '19 at 3:16
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    $\begingroup$ @dessind'efantterrible I cannot make a blanket statement. There exist questions where both tags would be appropriate, and there exist questions where the analysis tag would be inappropriate. Again, questions about the Hausdorff measure may not be relevant to the folk who are watching the analysis tag. The goal of tagging is to increase the visibility of a question among the users who may have the expertise and interest to answer. The abstract-algebra tag is read by a relatively large number of people, most of whom have little expertise in geometry. $\endgroup$ – Xander Henderson Oct 23 '19 at 3:17
  • $\begingroup$ @ArcticChar Replace analysis with real-analysis, and perhaps the analogy is more apt. In any event, the basic point is that there are some very general tags (such as analysis, abstract-algebra, or topology), and some very specific tags (such as dimension-theory, moduli-spaces, or knot-theory) which might fall under the scope of the more general tags. Specialized questions almost certainly should not be tagged with very general tags. $\endgroup$ – Xander Henderson Oct 23 '19 at 3:21
  • $\begingroup$ ok, i guess i have to defer to you guys although imo the harms of "cluttering" the more general tag seem clearly outweighed by the benefits of visibility on a site where there are hundreds of questions each hour . anyway heres hoping i dont have any burning hausdorff measure questions :) $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:41
  • $\begingroup$ @dessind'efantterrible The issue is not one of "cluttering" the more general tags. Rather, the issue is that someone who is following the more general tag (but not the more specific tag) is unlikely to be able to answer the question. Increasing the visibility of a question doesn't do much good if the people reading it don't know how to answer. As an extreme example, why not just tagger everything "mathematics"---surely everyone reading Mathematics is interested in mathematics, no? $\endgroup$ – Xander Henderson Oct 23 '19 at 3:45
  • $\begingroup$ @XanderHenderson genericity means there will be many posts that dont interest many followers. im interested in abstract algebra and analysis but if i go to those tabs i have any interest in engaging about 1 out of 30 questions. re: your extreme example-- yes clearly its a balance between lumping and splitting. i just think there are very negligible harms of lumping in cases such as this. $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:51
  • $\begingroup$ but it sounds like there are ad hoc convention about particular tags, which is perfectly fine. $\endgroup$ – dessin d'enfant terrible Oct 23 '19 at 3:53
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    $\begingroup$ I don't have the power to check on the mobile app, but I'd be surprised if anyone at all is following the tag hausdorff-measure. If you're looking to kill your visibility, using that tag and not including something more general is the way to go. $\endgroup$ – Matt Samuel Oct 23 '19 at 20:19
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    $\begingroup$ @MattSamuel There are actually five people following the hausdorff-measure tag. Given that the tag only has about 150 questions total, I would say that is a pretty good number. That being said, there are several tags of generality between "analysis" and "hausdorff-measure" which would be appropriate on a question about the Hausdorff measure–measure-theory, for example. $\endgroup$ – Xander Henderson Oct 24 '19 at 12:29

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