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edit approved Oct 24, 2013 at 14:45

class groups of unramified cyclic pp-extensions of imaginary quadratic fields

Let K$K$ be an imaginary quadratic number field with p$p$-Sylow-class group A(K)$A(K)$ and L/K$L/K$ be an unramified cyclic extension of K$K$ of degree p$p$ (p$p$ prime). Then I am looking for heuristics on

            Ker(N_{L/K}:A(L)\rightarrow A(K)), where

$ker(N_{L/K}:A(L)\rightarrow A(K))$,

where $N_{L/K}$ is the usual norm map on ideal classes. Numerical data suggest that:

$|KerN_{L/K}|\le p^2$ with high probability. But that is rather unprecise. Are there any more satisfactory known results ?

There is a result by Wittmann who gives some heuristics for cyclic p$p$-extensions of $\mathbb{Q}$ and I wonder if one can possibly generalize his ideas to the above scenario.

class groups of unramified cyclic p-extensions of imaginary quadratic fields

Let K be an imaginary quadratic number field with p-Sylow-class group A(K) and L/K be an unramified cyclic extension of K of degree p (p prime). Then I am looking for heuristics on

            Ker(N_{L/K}:A(L)\rightarrow A(K)), where

$N_{L/K}$ is the usual norm map on ideal classes. Numerical data suggest that:

$|KerN_{L/K}|\le p^2$ with high probability. But that is rather unprecise. Are there any more satisfactory known results ?

There is a result by Wittmann who gives some heuristics for cyclic p-extensions of $\mathbb{Q}$ and I wonder if one can possibly generalize his ideas to the above scenario.

class groups of unramified cyclic p-extensions of imaginary quadratic fields

Let $K$ be an imaginary quadratic number field with $p$-Sylow-class group $A(K)$ and $L/K$ be an unramified cyclic extension of $K$ of degree $p$ ($p$ prime). Then I am looking for heuristics on

$ker(N_{L/K}:A(L)\rightarrow A(K))$,

where $N_{L/K}$ is the usual norm map on ideal classes. Numerical data suggest that:

$|KerN_{L/K}|\le p^2$ with high probability. But that is rather unprecise. Are there any more satisfactory known results ?

There is a result by Wittmann who gives some heuristics for cyclic $p$-extensions of $\mathbb{Q}$ and I wonder if one can possibly generalize his ideas to the above scenario.

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asked Aug 17, 2011 at 12:00

Tobias Bembom

class groups of unramified cyclic p-extensions of imaginary quadratic fields

Let K be an imaginary quadratic number field with p-Sylow-class group A(K) and L/K be an unramified cyclic extension of K of degree p (p prime). Then I am looking for heuristics on

            Ker(N_{L/K}:A(L)\rightarrow A(K)), where

$N_{L/K}$ is the usual norm map on ideal classes. Numerical data suggest that:

$|KerN_{L/K}|\le p^2$ with high probability. But that is rather unprecise. Are there any more satisfactory known results ?

There is a result by Wittmann who gives some heuristics for cyclic p-extensions of $\mathbb{Q}$ and I wonder if one can possibly generalize his ideas to the above scenario.