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Collected Works of John Tate, Part I: (1951-1975)

Barry Mazur and Jean-Pierre Serre, editors
American Mathematical Society
Publication Date: 
Number of Pages: 
Collected Works 24
[Reviewed by
Fernando Q. Gouvêa
, on

John Tate won the Leroy P. Steele Prize for Lifetime Achievement in 1995, the Wolf Prize in 2002, and the Abel Prize in 2010, an impressive trifecta that shows the respect and admiration he has earned during his long career. That is probably recommendation enough: anyone interested in number theory will find many important papers here.

But there’s more: several previously unpublished papers are included, as well as selections from Tate’s famous correspondence. Thus, even those who have a fat folder full of Tate’s papers will want a copy.

And even more: Tate has added comments on most of the papers. These range from corrections and references to more personal notes. I particularly enjoy those that explain the genesis of a paper and the ones that say things such as “X wrote this paper. I don’t know why he put my name on it.” The papers are “ordered chronologically by the time they were written,” rather than by publication date.

As is well known, Tate has never been a prolific writer. In the introduction, he says

I did not write easily, and am thankful that my colleagues generously included unpublished results of mine in their papers and books, crediting me fully.

Nevertheless, his papers fill two big volumes. They are reproduced directly from the original sources, which almost always works well. The exceptions are two reports on the Fields Medals, originally published in Science, whose pages are both larger and in a different format. Luckily, both are quite short, so the reader only needs to squint (or use a magnifying glass) for a few pages.

Comparing the table of contents with the list of publications in The Abel Prize 2008–2012 reveals that a couple of things were not included: “Mutiplication complexe formelle dans les corps locaux,” a contribution to a CNRS volume called Les Tendences Géometriques en Algèbre et Théorie des Nombres from 1966, “On the conjectures of Birch and Swinnerton-Dyer and a geometric analog,” an “exposé” for Séminaire Bourbaki, and a few recent book introductions.

Both volumes open with a selection of photographs, including one taken at Tate’s 60th birthday conference that shows some of his many graduate students. A complete list of Tate’s students is included.

These are volumes to treasure.


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Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He was a graduate student at the time of the 1985 conference. His fat folder full of copies of Tate’s papers will be retired.