Here are some things that I’ve translated into English. Any comments or corrections are greatly appreciated. For contact details, see [thosgood.com]. 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 (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 Andrey Lushnikov’s LaTeX.Online), and 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.


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


Articles

Seminars

Séminaire Bourbaki

Extracts (1957–92), “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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Séminaire Claude Chevalley

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

  1. “Faisceaux quasi-cohérents” (P. Gabriel).
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  2. “Le théorème de Serre” (P. Gabriel).
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  3. “Les foncteurs dérivés des foncteurs classiques” (P. Gabriel).

  4. “Diviseurs en géométrie algébrique” (C.S. Seshadri).
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Séminaire Henri Cartan

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

Note that we have included any changes made in the Errata.

  1. “Sur la théorie de Kan” (H. Cartan).

  2. “Sur les faisceaux algébriques et les faisceaux analytiques cohérents” (A. Grothendieck).
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  3. “Sur le foncteur Hom(X,Y) en théorie simpliciale” (H. Cartan).

  4. “Théorie des fibrés principaux” (H. Cartan).

  5. “Les singularités des applications différentiables” (A. Haefliger).

  6. “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.)

  • (19/28) Grothendieck, A. “Géométrie formelle et géométrie algébrique”. (FGA 2)
    Séminaire Bourbaki 11 (1958–59), Talk no. 182.
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  • (8/19) Deligne, P. “A quoi servent les motifs?”.
    Proc. Symp. in Pure Math. 55 (1994), 143–161.
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  • (2/9) Hilbert, D. “Ueber die Darstellung definiter Formen als Summen von Formenquadraten”.
    Mathematische Annalen 32 (1888), 342–350.
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  • (4/31) 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.
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  • (12/126) Deligne, P. Equations Différentielles à Points Singuliers Réguliers.
    Springer-Verlag, LNM 163 (1970).
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  • (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
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  • (5/38) Grauert, H. “Über Modifikationen und exzeptionelle analytische Mengen”.
    Math. Ann. 146 (1962), 331–368.
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  • (3/40) 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.
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