In this paper we give an example of three wildly ramified extensions $L_1,L_2,L_3$ of $\Q_2$ with the same ramification numbers and isomorphic Galois groups, such that $I(nL_1)>I(nL_2)>I(nL_3)$ for a suitable integer $n$. This example shows that the condition given in \cite{galois} for the invariance of the index of tamely ramified extensions is no longer sufficient in the general case.
Non-invariance of the index in wildly ramified extensions
DEL CORSO, ILARIA;DVORNICICH, ROBERTO
2010-01-01
Abstract
In this paper we give an example of three wildly ramified extensions $L_1,L_2,L_3$ of $\Q_2$ with the same ramification numbers and isomorphic Galois groups, such that $I(nL_1)>I(nL_2)>I(nL_3)$ for a suitable integer $n$. This example shows that the condition given in \cite{galois} for the invariance of the index of tamely ramified extensions is no longer sufficient in the general case.File in questo prodotto:
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