English translations of mathematical articles, lecture notes, etc.
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 predating 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 selfcontained, 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 https://github.com/aslushnikov/latexonline), and the original (nonEnglish 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 https://github.com/ryankeleti/ega; 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.
Borel, A. and Serre, J.P. “Le théorème de RiemannRoch”.
Bulletin de la Société Mathématique de France 86 (1958), pp. 97–136.
DOI: 10.24033/bsmf.1500.
TeX

live PDF

original
Grothendieck, A. “La théorie des classes de Chern”.
Bulletin de la Société Mathématique de France 86 (1958) , pp. 137–154.
DOI: 10.24033/bsmf.1501.
TeX

live PDF

original
All of the following are by A. Grothendieck. A PDF copy of the original notes can be found at https://webusers.imjprg.fr/~leila.schneps/grothendieckcircle/FGA.pdf. 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.
Talk no. 1: “Faisceaux quasicohérents” (P. Gabriel).
TeX

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original
Talk no. 2: “Le théorème de Serre” (P. Gabriel).
TeX

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original
Talk no. 4: “Diviseurs en géométrie algébrique” (C.S. Seshadri).
TeX

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original
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.