Here are some things that I’ve translated into English. Any comments or corrections are greatly appreciated. I’ve tried to refrain from “rewriting” too much: generally the sentence structure etc. is pretty close to the original. Usually I don't have the time (or, truthfully, the energy) to fully proof-read everything after my first draft is done, so I'm sure that everything could be much improved. Sorry. Please contact me with any corrections or comments, either via email or via the GitHub repository: [thosgood/translations].

The following should go without saying, but I’ll say it anyway:
I am making no claim to any of the mathematics 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. All translations on this page are for personal use only.

The "Grothendieck trilogy"


  • M Balazard, E Saias, M Yor Notes sur la fonction ζ de Riemann, 2
    Adv. in Math. 143 1999 284–287
    PDF | TeX || original
  • A Borel, J-P Serre Le théorème de Riemann-Roch
    Bull. Soc. Math. Fr. 86 1958 97–136
    PDF | TeX || original
  • P Deligne Variétés abéliennes ordinaires sur un corps fini
    Inv. Math. 8 1969 238–243
    PDF | TeX || original
  • P Deligne Théorie de Hodge I
    Actes du Congrès intern. math. 1 1970 425–430
    PDF | TeX || original
  • P Deligne A quoi servent les motifs?
    Proc. Symp. in Pure Math. 55 1994 143–161
    PDF | TeX || original
  • Y Diers Catégories Multialgébriques
    Archiv der Math. 34 1980 193–209
    PDF || TeX
  • A Grothendieck La théorie des classes de Chern
    Bull. Soc. Math. Fr. 86 1958 137–154
    PDF | TeX || original
  • G Pólya Bemerkung Über die Integraldarstellung der Riemannschen ξ-Funktion
    Acta Math. 48 1926 305–317
    PDF | TeX || original

Séminaire Bourbaki

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.

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

The Grothendieck Circle has a PDF of the original notes. The translation below has been updated with the 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
    PDF | TeX
  2. Géométrie formelle et géométrie algébrique
    Séminaire Bourbaki 11 1958–59 Talk no. 182
    PDF | TeX
  3. Technique de descente et théorèmes d'existence en géométrie algébrique
    1. Généralités. Descente par morphismes fidèlement plats
      Séminaire Bourbaki 12 1959–60 Talk no. 190
      PDF | TeX
    2. Le théorème d'existence et théorie formelle des modules
      Séminaire Bourbaki 12 1959–60 Talk no. 195
      PDF | TeX
    3. Préschemas quotients
      Séminaire Bourbaki 13 1960–61 Talk no. 212
      PDF | TeX

Séminaire Claude Chevalley

Volume 4 (1958–59), Variétés de Picard
  1. P Gabriel Faisceaux quasi-cohérents
    PDF | TeX || original
  2. P Gabriel Le théorème de Serre
    PDF | TeX || original
  3. C S Seshadri Diviseurs en géométrie algébrique
    PDF | TeX || original
  4. A Douady Variétés abéliennes
    PDF | TeX || original

Séminaire Henri Cartan

Volume 9 (1956–57), "Quelques questions de topologie"
  1. A Grothendieck Sur les faisceaux algébriques et les faisceaux analytiques cohérents
    PDF | TeX || original
Volume 13 (1960–61), "Familles d'espaces complexes et fondements de la géométrie analytique"

The first talk [A Douady Fibrés en tores complexes] in the first volume of this seminar series was not written down; in the table of contents, a reference [M Atiyah Some examples of complex manifolds Bonner Math. Schrift. 6 1958 28 p] is given instead. Talks number 5 and 6 [C Houzel Modules des surfaces de Riemann] in the same volume were also not written down.

  1. A Douady Variétés et espaces mixtes
    PDF | TeX || original
  2. A Douady Déformations régulières
    PDF | TeX || original

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.)

  • (93/126) P Deligne Equations Différentielles à Points Singuliers Réguliers
    Springer-Verlag Lecture Notes in Mathematics 163 1970
    PDF | TeX || original
  • (1/29) A Grothendieck Technique de descente et théorèmes d'existence en géométrie algébrique IV: Schemas de Hilbert
    Séminaire Bourbaki 13 1960–61 Talk no. 221
    PDF | TeX
  • (7/19) A Douady Obstruction primaire à la déformation
    Séminaire Henri Cartan 13 (1) 1960–61 Talk no. 4
    PDF | TeX || original
  • (17/40) A Grothendieck Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires
    Annales de l'Institut Fourier 4 1952 73–112
    PDF | TeX || original
  • (11/31) M Brion, C Procesi 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
    PDF | TeX
  • (5/38) H Grauert Über Modifikationen und exzeptionelle analytische Mengen
    Math. Ann. 146 1962 331–368
    PDF | TeX || original
  • (10/214) P Deligne Le Groupe Fondamental de la Droite Projective Moins Trois Points
    In Galois Groups over ℚ, Springer-Verlag, MSRI Publications 16 1989 79–297
    PDF | TeX || 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! (I am particularly interested in finding some Spanish things to translate).

  • E Brieskorn Die Auflösung der rationalen Singularitäten holomorpher Abbildungen
    Math. Ann. 178 1968 255–270
  • P Deligne Théorie de Hodge II
    Pub. Math. de l'IHÉS 40 1971 5–58
  • P Deligne Théorie de Hodge III
    Pub. Math. de l'IHÉS 44 1974 5–77
  • Y Diers Catégories Localement Multiprésentables
    Archiv der Math. 34 1980 344–356
  • L Illusie Catégories dérivées et dualité
    L'Enseignement Math. 36 1990 369–391