All Questions
Tagged with class-field-theory ho.history-overview
7 questions
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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 $...
- 119
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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 ...
- 2,810
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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 ...
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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 ...
- 3,901
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The Teichmüller's algebraic interpretation of $H^3$ in group cohomology
In the book "Cohomology of Groups" of Kenneth S. Brown, it is told in the introduction that Teichmüller arrived to $H^3$ in an algebraic context, i.e. that Teichmüller worked with an ...
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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 ...
- 15.4k
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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 ...
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