The Stacks project

\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

How to contribute?

We welcome any kind of feedback: pointing out typos, mathematical errors, references in the literature, history of results, layout of webpages, spelling errors, improvements to the overall structure, missing lemmas, etc. In fact, there are several different ways you can help:

  1. If you are reading online and want to quickly point out something, please leave a comment on the tag's page. If possible please include your recommendation for how to change things.

  2. If you prefer, you can simply email us (see below).

  3. It is helpful if you edit the relevant TeX file directly and email the result. Even better: make a pull request (see below).

  4. We have a list of things you can do. Take a look!

  5. Unfortunately the sloganerator is inactive for the time being as it was incompatible with the new website. We will remedy this in the near future. Until then you can suggest slogans by leaving your suggestions as a comment.

  6. You are encouraged to email expository papers. It is extremely useful to have such a text (no matter how badly written) as the starting point for a new chapter. Please do not worry about coding style, errors, gaps in the exposition, etc. as the material will be radically changed anyway.

Please be aware that all contributions are licensed under the GNU Free Documentation License.

Where to submit?

Please email contributions to We will review, edit and if suitable update the Stacks project with your changes.

Please make pull requests here. We will review and merge your request if suitable or comment on your request otherwise.

Instructions on dealing with TeX files

You do not need to use Git in order to work directly with the TeX files.

  1. To download all TeX and supplementary files, download this this archive.
  2. Unpack the the archive.
  3. Edit the TeX file. Say algebra.tex.
  4. Run pdflatex algebra.tex, then bibtex algebra, and then pdflatex algebra.tex twice.
  5. Inspect the result and if OK then email algebra.tex to the address above.

An alternative to steps 1 and 2 is to download only the TeX file you want from git repository as well as preamble.tex and chapters.tex which are needed to compile it. Additionally you will need my.bib for the bibtex command to work.

Instructions on using the Makefile (slightly geeky)

Download and unpack the archive as above. Change directory to where you unpacked the files and on the command line type make pdfs to automatically generate all the pdf files. Use make dvis to generate the dvi files. The advantage of doing this over the simpler instructions above is that the cross file links will work.

Instructions on using a version control system (for major geeks)

We are using the git version control system. To clone the project type git clone on the command line. This assumes that you have git installed. For more information on using Git and GitHub, we refer to the documentation and GitHub Help. To actually contribute the changes you have made you use a pull request on GitHub. If you do not have a github account you can prepare a sequence of patches using git format-patch which you can email to the address above.