Let $K$ be a finite extension of $\Q_p$.
A **Galois splitting model** of $K$ is an irreducible polynomial $f\in\Q[x]$ such that $K\cong \Q_p[x]/(f)$, and the Galois group of $f$ over $\Q$ is isomorphic to the Galois group of $f$ over $\Q_p$.

Most, but not all, local number fields have Galois splitting models.

In this case, the computation of various invariants related to $K$, such as the Galois invariants, can be computed more easily using $f$.

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- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-22 07:40:48

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**History:**(expand/hide all)

- 2020-10-22 07:40:48 by Andrew Sutherland (Reviewed)
- 2019-05-03 23:38:57 by John Jones
- 2019-05-03 19:26:40 by John Jones (Reviewed)
- 2018-07-04 23:52:38 by John Jones

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