Maths translations


English translations of papers, 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, any categorical statement) 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

News on SGA and FGA translations “coming soon™” (with the latter coming sooner than the former, I imagine).

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 passage from one language to another.



Séminaire Claude Chevalley

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

Séminaire Henri Cartan

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

Séminaire Schwartz

Volume 1 (1953–54), “Produits tensoriels topologiques d’espaces vectoriels topologiques. Espaces vectoriels topologiques nucléaires”

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.