For everybody reading and using the Stacks project here is something to keep in mind:

Of course the results in a particular section or chapter do not cover all possible results about the topic discussed in that section or chapter.

First of all, taken literally, this is simply not possible. But even trying to do justice to a topic and mention all the wonderful things one can say, would slow down progress to a halt. Adding all possible deductions and recombinations of lemmas in the section and earlier ones also often takes too much work.

Instead what we try to do is as follows. Each time we broach a new topic we try to have a skeleton outline of the basic material. Often we do this when there is just one tiny result we want to use. Then over time, we come back to the section/chapter with more material as needed. Also, sometimes a result cannot be formulated or proved immediately because it needs more terminology or results proven later in the Stacks project. When this happens we try to put in a pointer to this material in the earlier section.

This has turned out to work fairly well. But if you find cases where it didn’t then please let us know. For example, if you find a case where some elementary results are being used which have no formulation in earlier chapters, then please let us know so we can fix that. On the other hand, if you have a result you would like to see mentioned, then send us a latex file with the actual math and we will consider it for inclusion. Thanks!

One thought on “Completeness

  1. Was this post and April 1 joke? No textbook is complete. In my opinion, no textbook should be “complete”, at least, not if it is going to be used by students to learn a subject for the first time. Once I tried teaching an intro grad course out of a textbook that was written more as an encyclopedia than a textbook. Before each lecture, I spent hours tracing forward through the book trying to determine which baroque lemmas would be used later and which would not. That was not the author’s fault: it was my fault for trying to teach out of a book that was not suitable for classroom use.

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