Individual mathematical letters (some later published, some not)
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-Wahnitzer 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.
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).
(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 to Faltings (June 27, 1983) - 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) ).
Scan of the original)
- The 1987 letter from Grothendieck to P. Blass accompanying
the prenotes for EGA V.
Collections of mathematical letters
- The Grothendieck-Serre correspondence: Published in French
by the SMF and in bilingual by the AMS, the published collection will
shortly become available directly from the site. Note that this collection is
a selection, not the complete correspondence.
- Grothendieck's letters to Mumford: To appear shortly in
a volume of Mumford's complete works, these letters will become available
from the site after a suitable publication delay.
- Grothendieck's letters to Ronnie Brown: To appear within a
year, appended to the publication of Pursuing Stacks, these
letters will become available from the site after a suitable publication