On the compositum of wildly ramified extensions
classification
🧮 math.NT
math.AG
keywords
cyclicextensionscompositumfiltrationramificationramifiedwildlyabhyankar
read the original abstract
We compute the ramification filtration on wildly ramified $p^2$-cyclic extensions of local fields of characteristic $p$. The ramification filtration on the compositum of two $p$-cyclic and $p^2$-cyclic extensions are also computed. As an application, some partial results towards Abhyankar's Inertia conjecture has been proved.
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