Mathematical letters by Grothendieck

• First second third fourth fifth sixth seventh and eighth letters to Dixmier from 1950 to 1955 (scans).
• First second third fourth fifth sixth seventh eighth letters to Dixmier from 1950 to 1955 (typed).
• First second third fourth fifth sixth seventh eighth exchange of letters between Grothendieck and Lipman, 1969-1970.
• Motives letter to Serre (August 8, 1964)- The English translation of a letter from from Grothendieck to Serre which contains his first written mention of motives. The original letter is published in Correspondance Grothendieck-Serre, Documents Mathématiques, Société Mathématique de France, 2001.
• Crystals letter to Tate (May 1966) - A 31-page letter from Grothendieck to Tate, in which the notion of crystals was born and baptized (with a nice ``commentaire terminologique'' about the name). It contains the conjectures, based on an analogy with the work of Monsky-Washnitzer in the affine case, on the comparison between crystalline and de Rham cohomology. For a first-hand historical survey of the theory (starting with the present letter), see the article by L.Illusie in Motives, Proceedings of Symposia in Pure Mathematics, Volume 55, 1994, Part 1, 43-70.
• Motives letter to Illusie (May 3, 1973)- A letter from Grothendieck to Luc Illusie containing remarks on motives. The original letter is published as an appendix to an article by Jannsen, in Vol. I (p. 296) of Motives (U. Jannsen et al. eds), Proc. Symp. Pure Math 55, AMS, 1994.
• Scans of three letters from Grothendieck to Larry Breen containing remarks on the yoga of homotopy (n-categories etc). Letter 1 (February 17, 1975, 5 pages)    Letter 2 (July 17-19, 1976, 22 pages + 4 pages of comments)    Letter 3 (April 8, 1982, 10 pages, page 4 unfortunately missing)
  The same letters in a smaller size suitable for printing:  Letter 1,  Letter 2,  Letter 3.
• Grothendieck's letters to Ronnie Brown, 1982-1991

• Anabelian letter to Faltings (June 27, 1983) - A typed-up version of a letter from Grothendieck to G. Faltings in German, describing Anabelian Algebraic Geometry. To Grothendieck's disappointment, Faltings never responded to this letter. However, Faltings' student Shinichi Mochizuki picked up the subject years later and proved Grothendieck's anabelian conjecture for hyperbolic curves. This letter was later published in Geometric Galois Actions I (P. Lochak and L. Schneps, eds., London Math Society Lecture Note Series 242, Cambridge University Press (2000) ). (English translation)  (Scan of the original)
• The 1987 letter from Grothendieck to P. Blass accompanying the prenotes for EGA V.
• A 1991 letter from Grothendieck to Robert Thomason in the original French and translated into English by Tim Hosgood.

Collections of mathematical letters

• The Grothendieck-Serre correspondence The correspondence was first published in French by the SMF, subsequently in a bilingual version by the AMS. The collection is in fact a selection, not the complete correspondence. Additional letters from the correspondence will shortly appear on this site.
• The Grothendieck-Mumford correspondence These letters have been published in Volume II of Mumford's complete works.