Maths translations


English translations of mathematical articles, lecture notes, etc.

View the Project on GitHub thosgood/translations

Here are some maths papers that I’ve translated into English. Any comments or corrections are greatly appreciated. For contact details, see my website. I’ve tried to refrain from “rewriting” too much: generally the sentence structure etc. is pretty close to the original. As a consequence, some of the language (in particular, certain phrases from papers pre-dating the standardisation of the language of category theory) is slightly wordy, but hey ho.

For each paper, there is a link to the .tex source file (and I’ve tried to keep these self-contained, i.e with internal bibliographies), a link to a PDF which is built from the latest version of the .tex file every time you load the page (many thanks to, and the original (non-English language) paper. Each PDF has a version number (the first 8 characters of the MD5 hash of the source code). This makes it easy to tell at a glance whether or not there have been any changes.

For translations of the EGA, see; for FGA translations, see below (under “Séminaire Bourbaki”); news on SGA translations “coming soon™”.

This should go without saying, but I’ll say it anyway: I am making no claim to any of the mathematics or ideas contained in any of these translations; the only things that are mine are the errors introduced during the hazardous journey from one language to another.



Séminaire Bourbaki

Extracts (1957–92), “Fondements de la Géométrie Algébrique”

All of the following are by A. Grothendieck. A PDF copy of the original notes can be found at We have taken the comments and errata from the May 1962 “Commentaires” (Séminaire Bourbaki 14, 1961–62, Complément) and inserted them into the relevant places in the notes themselves, making clear when this has been done.

Séminaire Claude Chevalley

Volume 4 (1958–59), “Variétés de Picard”

Séminaire Henri Cartan

Volume 9 (1956–57), “Quelques questions de topologie”

In progress

Some of the longer papers take a while to translate, but, once they reach a certain level of completion, I’ll share them here so that at least what I have done can be available. The papers that make up Grothendieck’s FGA will just be released one at a time when completed.