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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 $f$.

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