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Correspondance Serre-Tate, Volume I

Pierre Colmez and Jean-Pierre Serre, editors
Société Mathématique de France
Publication Date: 
Number of Pages: 
Documents Mathématiques
[Reviewed by
Fernando Q. Gouvêa
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Jean-Pierre Serre and John Tate are certain to be on any list of the greatest mathematicians of the second half of the twentieth century. Of the two, Serre is by far the more prolific; Tate, by contrast, has published very little, but is well known to be a great writer of letters. It is easy to see, then, that the letters exchanged by Serre and Tate since 1956 will of great interest to both mathematicians and historians of mathematics. The SMF’s Documents Mathématiques series scores another hit with these two volumes.

The editors have based their book on the letters in Serre’s archives, which contained Tate’s letters and carbon copies of most of Serre’s. From 1991 on, the correspondence was supplemented by email, and the editors tell us that they have included “those emails from the period 1991–2000 that survived the successive changes of computer.” After 2000 most of the correspondence moved to email, so “most of these have disappeared.” A few that did survive are included in a section entitled “Quelques échanges posterieurs.” A few other documents are also included: letters to other mathematicians, tables, etc.

The letters are presented with notes from Serre (labeled S1, S2, etc.) and notes by Colmez (labeled C1, C2, etc.). Serre’s notes tend to be quick references or explanations (and occasionally corrections), while Colmez typically writes more to set the conversation in context. These notes appear as endnotes in the second volume (probably the only editorial decision made here that I regret), so even those interested only in material included in the first volume will need to have both volumes. Volume two also includes a blibliography, a “thematic index” and an “index of proper names.”

The correspondence was conducted sometimes in French, sometimes in English, and the letters are reproduced here in their original languages. They were scanned and then turned into TeX by a large group of volunteers. They, the editors, and the SMF all deserve our thanks, as do, of course, Serre and Tate themselves. By agreeing to share these letters with the world, they allow us to know them and their mathematics better and open a window on the evolution of number theory and algebraic geometry over the last 60 years.

Fernando Q. Gouvêa had the privilege, long ago, of taking courses from both Jean-Pierre Serre and John Tate. 

The table of contents is not available.