What Is the Stacks project Website?

The Stacks project (stacks.math.columbia.edu) is an open-source textbook and reference work on algebraic geometry. It is aimed at readers who need a structured, citable body of definitions, lemmas, and proofs rather than a conventional narrative textbook. The site presents the material as a living document: content is organized into chapters and sections, individual results carry permanent tags, and changes are recorded publicly along with a blog and bibliography.

What the site contains

The project is large and reference-oriented. According to the site's own statistics, it currently consists of:

The "lines of code" figure reflects that the text is maintained as source files, which is consistent with an open-source, version-controlled reference work. "Slogans" are short informal summaries attached to results, useful when you want the gist before reading a full proof.

How the content is organized

The site's table of contents is the main entry point. Material is divided into chapters and then sections, and every individual result is assigned a tag such as 0BMA or 02K9. Tags matter for two reasons:

• They give you a stable identifier to cite or search for, even if surrounding text is reorganized.
• They let you jump directly to a specific lemma or definition instead of navigating the table of contents.

If you already know the tag, the search function is the fastest route. If you are exploring a topic, start from the table of contents and work down through chapters to sections.

Who maintains it and how it changes

The project is community-maintained, and the site makes its change history visible rather than hiding it:

• Recent comments list tag-level comments with dates and contributor names, for example a comment on tag 0BMA dated Oct 16 2026.
• Recent commits show content changes, such as "A couple of compatibilities for relative cycles" on 28 Jul 2026 or "Found the missing comma" on 14 Jul 2026.
• Recent blog posts cover project news and mathematical notes, including "Stacks project website slow" (22 May 2026) and "Nonflat deformation theory" (25 Jan 2026).

A GitHub link is provided on the site, which is the natural place to look if you want to follow or contribute to the source. The presence of dated comments and commits means you can judge how current a result is and see whether a specific tag has been discussed.

When this site is the right resource

Use the Stacks project when you need:

• A citable statement of a result in algebraic geometry, with a tag you can reference in your own work.
• A proof or definition at a level of generality beyond what a standard textbook covers.
• A way to check whether a lemma you need exists and how it is formulated.

It is less suited to readers who want a guided first course: the volume (over 7,600 pages) and the reference-style organization mean you generally need a specific question or topic in mind. For a first pass on a subject, a conventional textbook plus the project's table of contents as a lookup tool is usually the more practical combination.

Practical starting points

1. Browse by topic: open the table of contents and drill into the relevant chapter, then section.
2. Look up a known result: use search with the tag (for example 02K9) to land on the exact statement.
3. Check provenance: consult recent comments and commits to see whether a tag has been recently revised or discussed.
4. Follow project news: the blog carries updates on the site itself and on mathematical content.

One caveat worth knowing: the site has publicly noted performance problems ("Stacks project website slow," 22 May 2026), so if a page loads slowly, retrying later or using search to go directly to a tag can save time.