Here are some things that I’ve translated into English. In general, I try to refrain from restructuring them too much: the sentence structure, punctuation, etc. is pretty close to the original; when faced with a decision between "literal" and "fluid", I tend to opt for the former. In short, these translations are more mathematical than historical.
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! But please do contact me with any corrections or comments, either by email or through the relevant GitHub repository (where you can also find the full source code). The smaller translations are all kept at @thosgood/translations, but the bigger ones sometimes have their own repository.
If you want to read about these translations, then have a look at the translation tag on my blog.
Finally, 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 (human) use only.
Multilingual mathematical dictionary
As part of undertaking these translations, I started building a multilingual mathematical dictionary. Since sharing this online, I have received contributions in many languages from many wonderful volunteers. This is an ongoing project, but you can view the current version of the dictionary at ~/maths-dictionary.
Articles
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Notes sur la fonction ζ de Riemann, 2 Advances in Mathematics 143 1999 284–287
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Le théorème de Riemann-Roch Bulletin de la Société Mathématique de France 86 1958 97–136
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Variétés analytiques complexes et cohomologie Colloque sur les fonctions de plusieurs variables, Bruxelles 1953 41–53
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Variétés abéliennes ordinaires sur un corps fini Inventiones Mathematicae 8 1969 238–243
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Théorie de Hodge I, II, III I: Actes du Congrès International des Mathématiciens 1 1970 425–430
II: Publications Mathématiques de l'IHÉS 40 1971 5–58
III: Publications Mathématiques de l'IHÉS 44 1974 5–77 -
A quoi servent les motifs? Proceedings of Symposia in Pure Mathematics 55 1994 143–161
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Catégories Multialgébriques Archiv der Mathematik 34 1980 193–209
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Exemples de groupes differentiels: flots irrationnels sur le tore Comptes rendus de l'Académie des Sciences 301 1985 127–130
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Catégories doubles et catégories structurées Comptes rendus de l'Académie des Sciences 256 1963 1198–1201
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Catégories structurées Annales scientifiques de l'École normale supérieure 80 1963 349–426
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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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La théorie des classes de Chern Bulletin de la Société Mathématique de France 86 1958 137–154
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Bemerkung Über die Integraldarstellung der Riemannschen ξ-Funktion Acta Mathematica 48 1926 305–317
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Complexe dualisant et théorèmes de dualité en géométrie analytique complexe Publications Mathématiques de l'IHÉS 38 1970 77–91
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Automorfismo de foliaciones holomorfas sobre superficies racionales Pro Mathematica 16 2002 47–59
Seminars
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 (containing the first 49 talks, and dating from 1948 up until 1951) was printed in 1952.
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Les travaux de Koszul, I
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Les travaux de Koszul, II
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Les travaux de Koszul, III
Séminaire Claude Chevalley, Volume 4 (1958–59), "Variétés de Picard"
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Faisceaux quasi-cohérents
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Le théorème de Serre
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Diviseurs en géométrie algébrique
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Variétés abéliennes
Séminaire Henri Cartan, Volume 9 (1956–57), "Quelques questions de topologie"
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Sur les faisceaux algébriques et les faisceaux analytiques cohérents
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)]. The fifth and sixth talks (Houzel, C. "Modules des surfaces de Riemann") have suffered much the same fate, with the complete list of talks simply stating that they were not written down and will not be copied for distribution.
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Variétés et espaces mixtes
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Déformations régulières
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Obstruction primaire à la déformation
Books
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Equations Différentielles à Points Singuliers Réguliers Springer-Verlag Lecture Notes in Mathematics 163 1970
Letters
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Lettre d’Alexander Grothendieck sur les Dérivateurs, 02.04.91 Edited by Matthias Künzer.
EGA, FGA, SGA
The smallest of the three large treatises on algebraic geometry is finished (or, at least, a complete first draft is).
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Foundations of Algebraic Geometry (FGA)
The remaining two are really rather large indeed. Because of this, their translations form projects that will last for quite a few years yet to come. Neither of them is fully finished yet, nor will they be any time soon.
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Éléments de Géométrie Algébrique (EGA)
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Séminaire de Géométrie Algébrique du Bois-Marie (SGA)
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. The fractions show how many pages I've translated so far, and they are colour coded by percentage.
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T-categories (catégories dans un triple) Cahiers de Topologie et Géométrie Différentielle Catégoriques 12 1971 215–321
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Géométrie analytique locale, II. Théorie des morphismes finis Séminaire Henri Cartan 13 1960–61 Talk no. 19
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Dualité relative en géométrie analytique complexe Inventiones mathematicae 13 1971 261–283
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Le Groupe Fondamental de la Droite Projective Moins Trois Points In Galois Groups over ℚ, Springer-Verlag, MSRI Publications 16 1989 79–297
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Über formale komplexe Räume manuscripta mathematica 24 1978 253–293
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Über Modifikationen und exzeptionelle analytische Mengen Mathematische Annalen 146 1962 331–368
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Repartición de corriente en una red conductora. (Introducción al análisis combinatorio) Revista Matematica Hispano-Americana 5 1923 153–164
Wish list
Translations which I have yet to start, but "one day" intend to, are listed here. Feel free to contact me with any suggestions (though I definitely cannot commit to actually following through on any).
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Komplexe Räum Mathematische Annalen 136 1958 245–318
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Zur Theorie der Steinschen Algebren und Moduln Mathematische Zeitschrift 97 1967 376–405
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Relativ-analytische Räume und die Kohärenz von Bildgarben Inventiones mathematicae 16 1972 113–160
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Catégories dérivées et dualité L'Enseignement Math. 36 1990 369–391
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Groupes différentiels et physique mathématique Centre de Physique Théorique 83/P.1547 1983 1–47
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Cristaux discontinus
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Sur les modèles de la géométrie différentielle synthétique Cahiers de Topologie et Géométrie Différentielle Catégoriques 20 1979 231–279
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Sur les espaces (F) et (DF) Summa Brazil. Math. 3 1954 57–123
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Champs affines Selecta Mathematica 12 2006 39–134
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Images de faisceaux analytiques cohérents Séminaire Lelong, Analyse 1 1958 Talk no. 11
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Objets compacts dans les topos J. Austral. Math. Soc. 40 1986 203–217