Documents -- J.S. Milne
Documents - J.S. Milne, Top

Séminaire Heidelberg-Strasbourg 1965-66 (Groupes Algébriques)

Multigraphié par l'Institut de Mathématique de Strasbourg (Demazure, Gabriel, et al.). 407 pp.
These are the notes of a seminar led by Demazure and Gabriel, which was a precursor for their book "Groupes Algébriques", but the notes go further than the book in fewer pages. They are quite rough, and are in French and German, but I found them useful when writing my book on Algebraic Groups, and so I think they should be available. pdf

Letter of Deligne November 30, 2011

Shows that a Tannakian category over an algebraically closed field has a fiber functor (handwritten, 6 pages). Posted with permission (via Drinfeld). pdf

Notes of courses given by Tate in the 1960s

Arithmetic on Elliptic Curves, Spring 1960. pdf
Abelian Varieties, Fall 1962. pdf It was while teaching this course that Tate discovered his short proof of Neron's conjecture on the existence of a quadratic height.
Algebraic Functions (part), Spring 1965. pdf It was while teaching this course that Tate discovered his new approach to residues and differentials (Ann. Sci. ENS. 1968 149--159).
(Commutative) Formal Groups (part), Fall 1966. pdf This course led to the Tate-Oort paper (Ann. Sci. ENS. 1970 1--21).
Arithmetic on Elliptic Curves, Fall 1967. My copy of the notes is faint, and the scan is illegible, and so won't be posted.

Proceedings of the 1955 Tokyo-Nikko Conference on Algebraic Number Theory

This was perhaps the first major mathematics conference held in Japan. It was attended by most of the leading Western algebraic number theorists (Artin, Chevalley, Deuring, Serre, Weil, ...) as well as the new generation of young Japanese mathematicians (Iwasawa, Nakayama, Satake, Shimura, Taniyama, ...). The talks by Shimura, Taniyama, and Weil marked the birth of the theory of complex multiplication for abelian varieties of dimension greater than 1.
Photo with key

Automorphic Forms, Shimura Varieties, and L-functions, Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6--16, 1988.

A scan of this is available under Books. Posted with the permission of the publisher.

Deligne: Hodge cycles on abelian varieties (Notes by J.S. Milne)

This is a TeXed copy of Hodge cycles on abelian varieties (the notes of most of the seminar "Periodes des Integrales Abeliennes" given by P. Deligne at I.H.E.S., 1978--79; pp9--100 of Deligne et al. 1982, LNM 900) somewhat revised and updated with the addition of endnotes.

July 4, 2003 pdf

Deligne's famous letter to Piatetski-Shapiro, April 2, 1973.

Scan(pdf) A LaTeX transcription (without the covering letter) is available on Jared Weinstein's website here and another (without the covering letter and missing a line) at IAS.

Lecture notes prepared in connection with the seminars held at the Summer Institute on Algebraic Geometry, Whitney Estate, Woods Hole, Massachusetts, July 6 -- July 31, 1964

Complete file, bookmarked, 10MB.
"The summer institute gave us the idea that algebraic geometry was now a real subject, and no longer simply a mass of iffy results with a few valiant people like Zariski and Weil struggling to make order..." (Mumford)
In the summer of 1964, the AMS held a conference on Algebraic Geometry at Woods Hole, and distributed the informal mimeographed proceedings of the conference to a select few. Despite their great historical importance --- this was where Tate stated his conjectures on cycles, and they contain the only written statement by Artin and Verdier of their duality theorem and the only written account by Serre and Tate of their lifting theorem --- the AMS has ignored all requests to make the proceedings more widely available. Here (courtesy of Roy Smith), I've posted the complete notes. More...

1. Theory of Singularities (Abhyankar, Hironaka, Zariski); Classification of Surfaces and Moduli (Kodaira, Matsusaka, Mumford, Nagata, Rosenlicht, Igusa) pdf

2. Grothendieck Cohomology (Artin, Verdier, Tate); Zeta Functions and Arithmetic of Abelian Varieties (Cassels, Dwork, Shimura, Serre) pdf

3. Reports on various seminars, including: Artin and Verdier on their duality theorem for number fields; Lubin, Serre, and Tate on formal groups and the lifting of abelian varieties; and Atiyah and Bott on the Woods Hole Fixed Point Theorem. pdf

Grothendieck's Prenotes for EGA5

Many years ago, Piotr Blass was given Grothendieck's prenotes for EGA 5. Here is a scan of a photocopy of the notes that Piotr gave to me (apparently he has lost his own copy). The scan (at 400dpi) accurately captures the notes as given to me, but the quality of some pages is poor and some pages may be out of order.
The scan of Grothendieck's notes (pdf 16MB).

Here is a letter from Grothendieck to Piotr Blass concerning the notes:
Grothendieck's letter (html/bmp).

Here is an edited translation of the prenotes by Joseph and Piotr Blass, as TeXed by Dottie Phares (IAS). Apparently, they haven't been proofread, so there are some typos.
The Blass/Blass translation (pdf 662KB).

The translation was further polished by Stan Klasa and made available at the Ulam Quarterly.

Other notes of Grothendieck

Notes1 (pdf 1.6MB)
Notes2 (pdf 2.7MB)