How to Find a Specific Topic or Result in the Stacks Project

Updated

To find a specific topic or result in the Stacks project, start from the site's table of contents if you know the general area, or use search and the tag system if you already have a precise statement, lemma number, or tag in mind. The site is an open-source textbook and reference work on algebraic geometry, so its navigation is built around chapters, sections, and stable tags rather than around a single search box.

Browse by structure: table of contents

The table of contents is the right entry point when you know the broad subject but not the exact result. The project is organized into chapters, which are divided into sections. According to the site's own statistics, the current build contains 116 chapters and 3298 sections across 7654 pages.

A practical browsing pattern:

  1. Open the table of contents from the homepage.
  2. Identify the chapter matching your subject area.
  3. Scan the section titles inside that chapter before opening individual results.
  4. Use the section view to read definitions and lemmas in context, since results often depend on earlier material in the same section.

This is slower than search but more reliable when you are learning a topic rather than looking up a known statement.

Search and tags: locating a precise result

Every result in the project carries a stable alphanumeric tag, and the site reports 21446 tags. Tags are the most precise identifier available: they survive edits and renumbering, so a tag you note today should still resolve later.

Use search when you have:

  • A keyword or phrase from a definition or theorem statement.
  • A tag such as 0BMA or 02K9, which you can enter directly.
  • A partial reference from a paper or another source that cites the project by tag.

The tag system also supports cross-referencing: if a paper cites "Tag 0BMA," searching that tag takes you to the exact lemma or definition, independent of where it currently sits in the table of contents.

Choosing between browsing and searching

Situation Best entry point Why
You know the subject but not the statement Table of contents Chapters and sections give context and prerequisites
You have a tag from a citation Search by tag Tags are stable and unambiguous
You remember a phrase but not the location Search Keyword search spans the whole project
You want related results and updates Blog, bibliography, recent changes Shows commentary, references, and what changed recently

Bibliography, blog, and recent changes

The homepage links to a bibliography, a blog, and lists of recent changes, recent comments, and recent commits. These are useful in three ways:

  • Bibliography — find the external references behind a result or check what a section depends on.
  • Blog — read commentary and updates, for example posts on the website being slow, general updates, nonflat deformation theory, de Rham cohomology of an Artinian ring, and surjective maps from affine space.
  • Recent changes and comments — see which tags were recently discussed or edited. The homepage lists comment activity by tag, such as tag 0BMA, tag 0CJ1, and tag 02K9, alongside commit messages like "A couple of compatibilities for relative cycles" and "Small topology lemma."

If a result looks different from what a paper cites, checking recent changes and the relevant tag's comment history is a reasonable first step before assuming an error.

A concrete lookup example

Suppose a paper cites "Tag 02K9" for a lemma you need. Enter the tag in search, open the result, and read the surrounding section for definitions and hypotheses. If you instead only remember that the lemma concerns a topic in a particular chapter, open the table of contents, find that chapter, and scan its sections. The tag route is faster and exact; the browsing route gives you the context the citation assumes.

Common sticking points

  • Confusing section numbers with tags. Section numbers shift as the project grows; tags do not. Record tags, not page or section numbers, when you need a durable reference.
  • Searching too broadly. A single common term can return many hits across chapters. Add a distinctive phrase from the statement, or search the tag if you have one.
  • Skipping prerequisites. Results are written to depend on earlier material in the same chapter. If a statement seems to use unexplained notation, read backward in the section first.
  • Assuming the site is static. The project is actively edited, with recent commits and comments visible on the homepage, so a result's wording or placement can change even though its tag stays fixed.