Unpublished Mathematical Texts
A General Theory of Fibre Spaces with Structure Sheaf
- This early paper, written while Grothendieck was at the University of
Kansas on an NSF grant in 1955, was only published as an NSF research report.
Introduction au Langage Fonctoriel - These are scans from
77 pages of original typed notes from a lecture course given by Grothendieck
in Algiers in November 1965.
Motifs - Apart from some letters to Serre and others,
this preliminary text dating from 1965-1970 and handwritten (typed up by
later readers) is the only mathematical text that Grothendieck
can be said to have written on the subject of motives, outside of some
letters to Serre (Grothendieck-Serre Correspondence).
Tannakian notes - A 25-page text (undated -- 1960's?) from J. Milne's files, on Tannakian categories over
a field and the toolbox of liens, gerbes etc. It contains a discussion
of applications to isocrystals and Dieudonné-Manin theory.
de Barsotti-Tate et Cristaux de Dieudonné - Notes by M. Hakim
and J-P. Delale of a lecture course given
by Grothendieck at U. of Montreal in the summer of 1970.
- Introduction to Functorial Algebraic Geometry - Notes written
by Federico Gaeta at (the first part of) a 100-hour course given by Grothendieck
in Buffalo, NY in the summer of 1973. These are not based on prenotes by
Grothendieck and to some extent represent Gaeta's personal understanding of what was
La Longue Marche à travers la
théorie de Galois, Contents - Table of contents.
This manuscript, consisting of some nearly 800 hand-written double pages, dating
from 1981, was left behind with Grothendieck's other unpublished manuscripts
when he disappeared in 1991. Typed in Tex, it comes out to about 400 pages. It goes together
with a further 1000 pages or so of additional notes and sections which have not
yet been read or typed. Many of the major themes were summarised in the
1983 manuscript Esquisse d'un Programme (available from the main Mathematical Texts page).
La Longue Marche, Part Ia - La longue Marche
à travers la théorie de Galois, (sections 1-25)-
Not yet available.
La Longue Marche, Part Ib - La longue Marche
à travers la théorie de Galois, (sections 26-37, 110 typed pages)
La Longue Marche, Part II -
Part II of the Longue Marche (sections 38-53) has not yet been typed yet, except
for the very long section 49 (129 typed pages).
- Pursuing Stacks
- Scans of the 500 page 1983 text by Grothendieck. For some information
on how Pursuing Stacks came to be written, see the article by
- Les Dérivateurs-
Grothendieck's 1991 manuscript `Les dérivateurs'.
Scans of Grothendieck's prenotes for EGA 5 (171 pages)-
The prenotes were given to Piotr Blass by Grothendieck in 1987. The
pages are somewhat mixed up so start by consulting the
Table of Contents. See also the 1987 letter from Grothendieck to
P. Blass in the list of letters below. Links to the version of this
part of EGA typed, revised and published by P. Blass and S. Klasa
can be found on the published mathematical texts page.
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.