Completeness

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!