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October 17th, 2018, 10:06 AM   #1
Joined: Jul 2018
From: morocco

Posts: 26
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Math Focus: algebraic number theory
Ambiguous classes

Hello community :

Let $K(\sqrt d)/K$ a extension of algebraic number fields.

I am looking for a some references in which i can find the results/proofs about the group of ambiguous classes and the group of the strongly ambiguous classes of an extansion $K(\sqrt d)/K$.
especially :
1) $Am_s (L/K)=\{ [{ p_1 }^{ a_1 }....{ p_t }^{ a_t } ]_L: a_i\in \{0,1\}\}$ where $p_1,...,p_r$ are the ramified primes of $K(\sqrt d)/$ ramified in $K(\sqrt d)/K$

2) Are the ambiguous classes represented by the ideals of $K(\sqrt d)/K$ laying over the ramified primes of $K(\sqrt d)/K$ ??

3) wish you share with me some ideas that you have about these groups

Thank you
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