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 by email or through the GitHub repository @thosgood/translations (where you can also find all source files).

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.



  • M Balazard, E Saias, M Yor Notes sur la fonction ζ de Riemann, 2
    Adv. in Math. 143 1999 284–287
    HTML | PDF || original
  • A Borel, J-P Serre Le théorème de Riemann-Roch
    Bull. Soc. Math. Fr. 86 1958 97–136
    HTML | PDF || original
  • P Deligne Variétés abéliennes ordinaires sur un corps fini
    Inv. Math. 8 1969 238–243
    HTML | PDF || original
  • P Deligne Théorie de Hodge I
    Actes du Congrès intern. math. 1 1970 425–430
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  • P Deligne A quoi servent les motifs?
    Proc. Symp. in Pure Math. 55 1994 143–161
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  • Y Diers Catégories Multialgébriques
    Archiv der Math. 34 1980 193–209
    PDF | TeX
  • 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
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  • A Grothendieck La théorie des classes de Chern
    Bull. Soc. Math. Fr. 86 1958 137–154
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  • G Pólya Bemerkung Über die Integraldarstellung der Riemannschen ξ-Funktion
    Acta Math. 48 1926 305–317
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  • P Deligne Equations Différentielles à Points Singuliers Réguliers
    Springer-Verlag Lecture Notes in Mathematics 163 1970
    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.

Séminaire Claude Chevalley, Volume 4 (1958–59), "Variétés de Picard"
  1. P Gabriel Faisceaux quasi-cohérents
    HTML | PDF || original
  2. P Gabriel Le théorème de Serre
    HTML | PDF || original
  3. C S Seshadri Diviseurs en géométrie algébrique
    HTML | PDF || original
  4. A Douady Variétés abéliennes
    HTML | PDF || original
Séminaire Henri Cartan, Volume 9 (1956–57), "Quelques questions de topologie"
  1. A Grothendieck Sur les faisceaux algébriques et les faisceaux analytiques cohérents
    HTML | PDF || original
Séminaire Henri Cartan, Volume 13 (1960–61), "Familles d'espaces complexes et fondements de la géométrie analytique"

The first talk (Douady, A. "Fibrés en tores complexes") of the 1960–61 Séminaire Henri Cartan appears to have been lost to the past: the complete list of talks from the edited second edition says that no copies of the notes were made, suggesting that the reader instead refer to an article [Atiyah M.F. "Some examples of complex manifolds". Bonner math. Schrift. 6 (1958)]. Here I have translated the next three talks.

The "Grothendieck trilogy"

The three large treatises on algebraic geometry are all, well, large. Because of this, their translations form projects that will last for quite a few years yet to come. None of them are fully finished yet, nor will they be any time soon.

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.)

  • A Grothendieck Lettre d’Alexander Grothendieck sur les Dérivateurs, 02.04.91 Edited by Matthias Künzer.
    HTML | PDF || original
  • A Grothendieck Technique de descente et théorèmes d'existence en géométrie algébrique IV: Schemas de Hilbert
    Séminaire Bourbaki 13 1960–61 Talk no. 221
  • J Bingener Über formale komplexe Räume
    manuscripta mathematica 24 1978 253–293
    HTML | PDF || original
  • 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
  • H Grauert Über Modifikationen und exzeptionelle analytische Mengen
    Math. Ann. 146 1962 331–368
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  • 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
    HTML | PDF || 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).

  • 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
  • P Deligne Multizetas, d'après Francis Brown
    Séminaire Bourbaki 64 2011–2012 Talk no. 1048
  • E J Dubuc Sur les modèles de la géométrie différentielle synthétique
    Cahiers de Topologie et Géométrie Différentielle Catégoriques 20 1979 231–279
  • H Grauert and R Remmert Komplexe Räum
    Mathematische Annalen 136 1958 245–318
  • A Grothendieck Sur les espaces (F) et (DF)
    Summa Brazil. Math. 3 1954 57–123
  • L Illusie Catégories dérivées et dualité
    L'Enseignement Math. 36 1990 369–391
  • B Toën Champs affines
    Selecta Mathematica 12 2006 39–134