nLab Esquisse d'un programme

Subtitle: a sketch of a programme

This was a document produced by Alexander Grothendieck that outline a series of interrelated research projects, (see the Wikipedia page).

Summary of Grothendieck’s programme

(English translation with original in brackets.)

(“Sommaire”)

1. The Proposal and enterpise (“Envoi”).

2. “Teichmüller’s Lego-game and the Galois group of Q over Q” (“Un jeu de ”Lego-Teichmüller“ et le groupe de Galois de Q sur Q”).

   (on the relation between the absolute Galois group and the Grothendieck-Teichmüller group)

3. Number fields associated with “children's drawings”. (“Corps de nombres associés à un dessin d'enfant”).

4. Regular polyhedra over finite fields (“Polyèdres réguliers sur les corps finis”).

5. Denunciation of so-called “general” topology, and heuristic reflections towards a so-called “tame” topology. (“Haro sur la topologie dite ‘générale’, et réflexions heuristiques vers une topologie dite ‘modérée”).

6. Differentiable theories and moderated theories (“Théories différentiables” (à la Nash) et “théories modérées”).

7. Pursuing Stacks (“À la Poursuite des Champs”}.

8. Two-dimensional geometry (“Digressions de géométrie bidimensionnelle”.

9. Summary of proposed studies (“Bilan d’une activité enseignante”).

10. Epilogue.

Notes

References

• A copy of the original version is here.

• An English translation is here.

• MO discussion

• Notes Anabéliennes de A. Grothendieck link