The Brauer-Hasse-Noether Theorem in Historical Perspective

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November 2004



The legacy of Helmut Hasse, consisting of letters, manuscripts and other - pers, is kept at theHandschriftenabteilung of the University Library at Gottin- ¿ gen.Hassehadanextensivecorrespondence;helikedtoexchangemathematical ideas, results and methods freely with his colleagues. There are more than 8000 documents preserved. Although not all of them are of equal mathematical - terest, searching through this treasure can help us to assess the development of Number Theory through the 1920's and 1930's. Unfortunately, most of the correspondence is preserved on one side only, i.e., the letterssenttoHasse are availablewhereasmanyoftheletterswhichhadbeensentfromhim,oftenha- written, seem to be lost. So we have to interpolate, as far as possible, from the repliestoHasseandfromothercontexts,inorderto?ndoutwhathehadwritten 1 in his outgoing letters. The present article is largely based on the letters and other documents which I have found concerning the Brauer-Hasse-NoetherTheorem in the theory of algebras; this covers the years around 1931. Besides the do- ments from the Hasse and the Brauer legacy in Gottingen, ¿ I shall also use some letters from Emmy Noether to Richard Brauer which are preserved at the Bryn Mawr College Library (Pennsylvania, USA).


The Main Theorem: Cyclic Algebras.- The Paper: Dedication to Hensel.- The Local-Global Principle.- From the Local-Global Principle to the Main Theorem.- The Brauer Group and Class Field Theory.- The Team: Noether, Brauer and Hasse.- The American Connection: Albert.- Epilogue: Käte Hey.



The author is Professsor emeritus at the University of Heidelberg, Germany. He is a member of the Heidelberger Academy of Sciences and of the Academy Leopoldina at Halle. He has been awarded an honorary doctors degree from the University of Essen.


From the reviews:
"The Brauer-Hasse-Noether theorem, as it has come to be known, is one of the few for which we have a precise birth date: all evidence points to November 9, 1931 ... . Roquette's account is quite interesting ... . Any mathematician who wants to understand why a number theorist would get excited about a theorem dealing with division algebras will find the issue well explained. I learned a lot by reading it ... ." (Fernando Q. Gouvêa, MathDL - Online, October, 2006)
"This fascinating monograph is devoted to the genesis of one of the most famous articles in 20th-century number theory ... . Roquette gives a very clear picture of the structure of the proof and the main ideas involved in it. Thus the text is not just a historical overview but also a valuable piece of mathematical exposition. ... All in All, this is a fascinating case study of the evolution of groundbreaking mathematical ideas." (Tamás Szamuely, Mathematical Reviews, Issue 2006 m)
EAN: 9783540230052
ISBN: 354023005X
Untertitel: 2005. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: November 2004
Seitenanzahl: 100 Seiten
Format: kartoniert
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