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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
18 votes
5 answers
2k views

What is the "ray" in ray class group?

I have never seen any algebraic number theory book discuss the origin of the term "ray class group." Does anyone know where the word "ray" comes from in this context? I always thought it might be a ...
David Corwin's user avatar
  • 15.4k
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
5 votes
2 answers
550 views

Compare with Weber and Hilbert class field

Heinrich Martin Weber and David Hilbert created their own class fields in 1891 and 1897 respectively. In the past, Weber continued to name $K={Q}(\sqrt{-m}, j(\omega))$, the Kronecker class field of $...
pokssin's user avatar
  • 119