If you think it has been awfully quiet on my weblog, you are correct. Three reasons: graduating, and sheer laziness. The third? Our new baby!

Little over a year ago I wrote a post with a remarkably similar title: A new website for the Stacks project. The last couple of months Johan and I have been working on a new version of the Stacks project website, and this morning we have finally released it!

So head your browsers at stacks.math.columbia.edu/!

Other announcements
What have we done?

Other announcements

What have we done?

New layout

I haven't turned into a designer in the past year, but we have updated the layout to a two-column version to accomodate all the new information we have incorporated in the new website (see next). And in general we have made improvements to the layout: better spacing, using the Stacks logo, using icons, ...

Tag lookup

We have updated the tag lookup page to incorporate more navigation options. Because that is what makes the Stacks project different from a usual book: it is online, and everything is linked.


The bibliography page is now easier to navigate. And each bibliography item now tells you where it is used, and it gives you the necessary BibTeX code to cite this result yourself.

Better search

The functionality of the search hasn't changed significantly, but the options now reflect they way we think the search functionality should work. And the previewing of tags has improved. And the chapters are now visible in the search results, which I think is a small but important improvement.


Everywhere it makes sense we have added statistics. Some of them are for showing off (e.g. on the main page), some of them provide new insights in the information contained in the Stacks project (e.g. if you want to know where Nakayama's lemma is used in the Stacks project). Together with the next point, these provide truly new ways of understanding the structure which is hidden in the Stacks project, and they provide new means of navigating the Stacks project.


This is the true highlight of the new version of the website. Dependency graphs. It is now possible to visualise how a result is built using earlier results.

Ever wanted to see how you can prove Hilberts Nullstellensatz? Now you can! Use your mouse to see the statements, change the colouring depending on whether you want to see the structure of the graph more clearly, or whether you want to see where the theorems, lemmas and definitions are hidden.

Ever wanted to see whether the proofs for Zariski's main theorem and Chow's lemma use results from the same chapters? Now you can! Answer: they don't, Zariski's main theorem uses virtually only results from the chapter on commutative algebra, while Chow's lemma is a truly geometric result, using results from both the algebra chapter (you need some algebra of course) but also purely geometric chapters.

And if the graphs for some of the results become too big (either for your browser, or for the human mind to interpret) you can use the clustered view, e.g. for the existence of residual gerbes. This way you can still see the main lines of the argument by the number of descendant tags (given in the mouseovers). For instance, a quick tour through this graph (click on nodes!) one learns that this result (down a few levels) could be considered as one of the key points, because it combines several arguments: it has significantly more descendant tags than each of its children.

These are just a few of the ways one can use these graphs. At some point we will write something about how we envision these being used. Feel free to find your own uses!


There are still bugs in the website. Some I am aware of, probably plenty I have no idea about. If you see something: send a mail to stacks.project@gmail.com, or even better: create an issue at stacks/stacks-website. This way the rest of the world immediately sees which bugs have been found.


I would like to thank everyone who participated in this process:

  • Johan, for his ideas, coding support and motivation
  • Cathy O'Neil, for her insistence on visualising the Stacks project, and her excellent comments on the first drafts of the graphs
  • Peter Woit, for being the perfect server admin
  • all the people at Columbia University, who made my breaks from coding so pleasant
  • everyone who contributed to all the open-source projects we are using