Here are some things that I’ve translated into English. Any comments or corrections are greatly appreciated. For contact details, see I’ve tried to refrain from “rewriting” too much: generally the sentence structure etc. is pretty close to the original.

For each paper, there is a link to the .tex source file, to a PDF which is built from the latest version of the .tex file every time you load the page (many thanks to Andrey Lushnikov’s LaTeX.Online), and to the original paper (if a copy is freely available online).

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.

The GitHub repository from which this website is built can be found at [thosgood/translations].

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.

The Grothendieck “trilogy”



Séminaire Bourbaki

Extracts (1957–62), “Fondements de la Géométrie Algébrique”

A PDF copy of the original notes can be found at The Grothendieck Circle. We have included any comments and errata from the May 1962 “Commentaires” (Séminaire Bourbaki 14, 1961–62, Complément).

All of the following are by A. Grothendieck.

  1. “Théorème de dualité pour les faisceaux algébriques cohérents”.
    Séminaire Bourbaki 9 (1956–57), Talk no. 149.
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  2. “Géométrie formelle et géométrie algébrique”.
    Séminaire Bourbaki 11 (1958–59), Talk no. 182.
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Extracts (1948–49), “Les travaux de Koszul”

In the first series of the Séminaire Bourbaki, H. Cartan gave three talks concerning the work of J.-L. Koszul on Lie algebras. (These specific talks were given in 1948–49, but the first published Séminaire Bourbaki collection was printed in 1952, containing the first 49 talks, and dating from 1948 up until 1951). I have combined all three talks into one document.

Séminaire Claude Chevalley

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

Séminaire Henri Cartan

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

  • Talk no. 2, “Sur les faisceaux algébriques et les faisceaux analytiques cohérents” (A. Grothendieck).
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  • Talk no. 7, “Les singularités des applications différentiables” (A. Haefliger).

  • Talk no. 8, “Un théorème de Thom sur les singularités des applications différentiables” (A. Haefliger and A. Kosinski).

In progress

Sometimes a paper takes “a while” to translate, but I put it here so that people can nudge me if there’s one on this list that they really want me to get around to finishing. (Some of these I have barely started, so don’t get too excited.)

  • (43/126) Deligne, P. Equations Différentielles à Points Singuliers Réguliers.
    Springer-Verlag, LNM 163 (1970).
    code-icon TeX | pdf-icon live PDF | file-icon original

  • (23/29) Grothendieck, A. “Technique de descente et théorèmes d’existence en géométrie algébrique. I. Généralités. Descente par morphismes fidèlement plats”. (FGA 3.I)
    Séminaire Bourbaki 12 (1959–60), Talk no. 190.
    code-icon TeX | pdf-icon live PDF

  • (6/31) Brion, M. and Procesi, C. “Action d’un tore dans une variété projective”.
    In Operator algebras, unitary representations, enveloping algebras, and invariant theory (Paris, 1989), Birkhäuser Boston, Progress in Mathematics 92 (1990), 509–539. MR1103602.
    code-icon TeX | pdf-icon live PDF

  • (5/38) Grauert, H. “Über Modifikationen und exzeptionelle analytische Mengen”.
    Math. Ann. 146 (1962), 331–368.
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  • (8/40) Grothendieck, A. “Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires”.
    Annales de l’Institut Fourier 4 (1952), 73–112.
    code-icon TeX | pdf-icon live PDF | file-icon original

  • (7/214) Deligne, P. “Le Groupe Fondamental de la Droite Projective Moins Trois Points”.
    In Galois Groups over ℚ, Springer-Verlag, MSRI Publications 16 (1989), 79–297. DOI: 10.1007/978-1-4613-9649-9_3
    code-icon TeX | pdf-icon live PDF | file-icon original

  • (2/9) Hilbert, D. “Ueber die Darstellung definiter Formen als Summen von Formenquadraten”.
    Math. Ann. 32 (1888), 342–350.
    code-icon TeX | pdf-icon live PDF | file-icon original

Wish list

Translations which I have yet to start, but one day intend to, are listed here, so that I don’t forget about them. Feel free to contact me with any suggestions!