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64 votes
3 answers
5k views

Class field theory - a "dead end"?

I found the claim in the title a bit astonishing when I first read it recently in an interview with Michael Rapoport in the German magazine Spiegel (8 February 2019). And I was wondering how he comes ...
wood's user avatar
  • 2,810
24 votes
1 answer
3k views

On the history of the Artin Reciprocity Law

At the beginning of Milne's notes on class field theory, he has a quote by Emil Artin (as recalled by Mattuck in Recountings: Conversations with MIT mathematicians): I will tell you a story about ...
Asvin's user avatar
  • 7,746
10 votes
4 answers
2k views

Origins of functional field arithmetic

Background: By function field, we mean a finite extension of the field of rational functions of one variable over a finite field with $p$ elements. Classfield theory for function fields was ...
Regenbogen's user avatar
  • 1,417
10 votes
1 answer
449 views

What are "Artin fractions"?

The German Wikipedia entry for Ernst Witt https://de.wikipedia.org/wiki/Ernst_Witt has a photo of his grave in Hamburg. The bottom part has a visible text "Artin Brueche" (Artin fractions) but the ...
Andrew Ranicki's user avatar