Each tag refers to a unique lemma, theorem, etc. in order for this project to
be referenceable. These tags don't change even if the lemma (or theorem, etc.)
moves within the text.

To look up a lemma, theorem etc. using a tag, just go to the search page and
input the tag in the box. To reference a result in the stacks project find its corresponding tag by
hovering/clicking on the lemma, theorem, etc. in the online pdf file. See below
for latex instructions.

The tag system provides stable references to definitions, lemmas, propositions,
theorems, remarks, examples, exercises, situations and even equations, sections
and items. As the project grows, each of these gets a tag which will always
point to the same mathematical result. The place of the lemma in the document
may change, the lemma may be moved to a different chapter, but its tag always
keeps pointing to it. If it ever turns out that a lemma, theorem, etc. was wrong then we may remove
it from the project. However, we will keep the tag, and there will be an
explanation for its disappearance (in the file tags mentioned below).

In your bibtex file put
@MISC{stacks-project,
        AUTHOR = "The {Stacks Project Authors}",
        TITLE = "{\itshape Stacks Project}",
        HOWPUBLISHED = "\url{http://math.columbia.edu/algebraic_geometry/stacks-git}",
}
Then can use a construction such as \cite[Definition 0123]{stacks-project} to reference the tag. If you feel couragous you can go ahead and make 0123 a
link to the stable url by the following construction \href{http://math.columbia.edu/algebraic_geometry/stacks-git/locate.php?tag=0123}{0123}

There is a file called tags (in the tags subdirectory) which has on each line
the tag followed by an identifier. Example:
        01MB,constructions-lemma-proj-scheme
Here the tag is 01MB and the identifier is constructions-lemma-proj-scheme.
This means that the tag points to a lemma from the file constructions.tex.
It currently has the label lemma-proj-scheme. If we ever change the lemma's
label, or move the lemma to a different file, then we will change the
corresponding line in the file tags by changing the identifier correspondingly.
But we will never change the tag.
New tags are assigned by the maintainer of the project every once in a while
using a script. A tag is a four character string made up out of digits and
capital letters. They are ordered lexicographically between 0000 and ZZZZ
giving 1679616 possible tags. That should be enough for a while!