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Results tagged with class-field-theory
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user 26522
7
votes
Accepted
Finite Nontrivial Unramified Towers of Number Fields
It is certainly possible that $1 < [L:F] < \infty$, i.e. that the extension $F^{\mathrm{un}}/F$ be finite and non-trivial. The simplest example of this is $F = \mathbb{Q}(\sqrt{-5})$. Its Hilbert clas …
- 13.8k
11
votes
Shortest/Most elegant proof for $L(1,\chi)\neq 0$
Here is an elementary proof, the basic idea for which is in Selberg's 1949 paper "An elementary proof of Dirichlet's theorem about primes in an arithmetic progression" (Ann. Math., vol 2, 1949, pp. 29 …
- 13.8k
11
votes
0
answers
373
views
What are the possible bad reductions for an abelian variety of dimension $g$ and a maximal e...
Perhaps the most basic fact about abelian varieties with CM is they have an everywhere potential good reduction (Serre-Tate). On the face of it it might appear that there isn't much more to be added t …
- 13.8k