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Emil Artin and John Tate held a seminar on class field theory at Princeton University in 1951--1952. Their notes were published in 1967 by Benjamin (New York), but the first four chapters covering (among other things) "the fundamentals of algebraic number theory" and "local class field theory" were omitted from the printed version.

Question. Are the notes of Chapters 1--4 available to you ?

Request. Can you make them electronically accessible to the mathematical community ?

Postscript. Parts of Hasse's Klassenkörperbericht (Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper) are available online at the Göttingen library :

Jber. deutsch. Math.-Verein. Teil I : 35 (1926), 1--55, Teil Ia : 36 (1927), 233--311.

Ulf Rehmann (Bielefeld) and Keith Dennis (Cornell) have promised to put Teil II (Jber. deutsch. Math.-Verein., Ergänzungsband 6 (1930), 1--204) online soon.

Addendum. In an interview which has appeared recently in the Notices of the AMS, Tate makes some remarks about the genesis of the Artin-Tate notes.

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    $\begingroup$ As far as I know, the notes for the first part of the seminar were never written up. Lang missed this part of the seminar because he started as a philosophy student. $\endgroup$
    – JS Milne
    Commented Oct 14, 2010 at 14:45
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    $\begingroup$ The Preface to Artin's book "Algebraic numbers and algebraic functions" (especially the timing indicated there), along with the list of topics in the book, make it seem plausible that it may be more or less that missing material. Check it out on Amazon. $\endgroup$
    – BCnrd
    Commented Oct 14, 2010 at 14:52
  • $\begingroup$ I agree. Another piece of evidence is the fact that this book began life as notes mimeographed by New York University, and Tate in his 1952 Annals paper lists "E. Artin and J. Tate, Algebraic Numbers and Algebraic Functions I and II, Notes, New York University" in his bibliography. $\endgroup$
    – Chandan Singh Dalawat
    Commented Oct 14, 2010 at 15:08

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In his preface to "Rapport sur la Cohomologie des Groups", Serge Lang says that those notes "provided missing chapters to the Artin-Tate notes on class field theory". It is available in english translation under the title "Topics in the cohomology of groups".

Edit: So perhaps Lang writing that it providing missing chapters does not mean that it provides ALL missing chapters.

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  • $\begingroup$ I had always thought that this report was written for Bourbaki. This is confirmed by Shatz in Math Reviews, who adds that "it provides a portion of the material missing from the Artin-Tate notes on class field theory [and] (in more or less their original form) some of the private papers of J. Tate". It is thus clear this Rapport does not contain everything from Chapters 1--4 of Artin-Tate. $\endgroup$
    – Chandan Singh Dalawat
    Commented Oct 14, 2010 at 12:15
  • $\begingroup$ Hochschild (Bull. Amer. Math. Soc. 75 (1969), 927--929) notes that "this is a report written in 1959 for the use of Bourbaki... the account given here contains everything from cohomology theory that is used in the well-known Artin-Tate treatment of class field theory, an unpublished portion of which is one of the sources of the present book". $\endgroup$
    – Chandan Singh Dalawat
    Commented Oct 14, 2010 at 12:15

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