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Thomas Riepe
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My experience was similar to that of David Speyer. My first encounter with class field theory was the very motivating "Introduction to the construction of class fields" by H. Cohn. That book motivates through questions on rational triangles, primes represented by quadratic forms, analogies from Riemann surfaces and the use of modular forms, Klein's icosahedron. An other very motivating aspect of it is the topological idea behind Kato's generalization, describing $\pi_1^{ab}$ of a scheme in different ways, and the geometry associated with that and ${\mathbb{F}}_1$-yoga. Conc. the cohomological approach, my impression was opposite to that of Arminius.

My experience was similar. My first encounter with class field theory was the very motivating "Introduction to the construction of class fields" by H. Cohn. That book motivates through questions on rational triangles, primes represented by quadratic forms, analogies from Riemann surfaces and the use of modular forms, Klein's icosahedron.

My experience was similar to that of David Speyer. My first encounter with class field theory was the very motivating "Introduction to the construction of class fields" by H. Cohn. That book motivates through questions on rational triangles, primes represented by quadratic forms, analogies from Riemann surfaces and the use of modular forms, Klein's icosahedron. An other very motivating aspect of it is the topological idea behind Kato's generalization, describing $\pi_1^{ab}$ of a scheme in different ways, and the geometry associated with that and ${\mathbb{F}}_1$-yoga. Conc. the cohomological approach, my impression was opposite to that of Arminius.

Source Link
Thomas Riepe
  • 10.8k
  • 5
  • 62
  • 92

My experience was similar. My first encounter with class field theory was the very motivating "Introduction to the construction of class fields" by H. Cohn. That book motivates through questions on rational triangles, primes represented by quadratic forms, analogies from Riemann surfaces and the use of modular forms, Klein's icosahedron.