Higher Math: Algebraic Number Theory and Class Field Theory
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- Pontryagin duals: see Poonen's notes on Tate's thesis, for instance.
By Victor Wang
- When is the (absolute) norm of an ideal actually the norm of an element? Principal ideal (may have unit/positivity issues) Ideal class is a square (always works!) How is this re…
By Victor Wang
- Connection from Kummer theory to class field theory. Also cyclotomic extensions...
By Victor Wang
- Understand this comment of KConrad: For a finite extension of number fields, the story is similar: ramification indices of all prime ideals over the same prime must be the same.…
By Victor Wang
- Sheaves of differentials Nice to have different perspectives. See even Neukirch for "arithmetic Riemann-Roch theory" (including a notion of genus of number field, and so on). Wa…
By Victor Wang
- Krasner's lemma and finite extensions of Qp\mathbb{Q}_pQp See MSE: Intuition for Krasner's Lemma for the key ingredient.
By Victor Wang
- A compactness theorem for the idele group See BCnrd's notes, Math 676. A compactness theorem for the idele group: The proof will be uniform across all global fields, and the key…
By Victor Wang
- Riemann-Roch over arbitrary fields See MO: Is there a Riemann-Roch for smooth projective curves over an arbitrary field? or a book on function fields, like Stichtenoth, Algebrai…
By Victor Wang, Victor Wang
- Dirichlet theorem, Frobenius density theorem, Chebotarev density theorem See MO: Frobenius density theorem discussion.
By Victor Wang