Summary: Let \(K\) be a global field and \(X,Y\) two proper, connected \(K\)-schemes, with \(X\) normal and \(Y\) regular. Let \(f:X\to Y\) be a finite, flat, generically Galois \(K\)-morphism which is tamely ramified along a normal crossings divisor on \(Y\). For closed points \(y\in Y\) outside of the branch locus of \(f\) and points \(x\in f^{-1}(y)\), we use the ‘geometric’ inertia groups of \(f\) and intersection numbers involving \(y\) and the branch locus in order to compute the ‘arithmetic’ inertia groups in \(\text{Gal}(K(x)/K(y))\) at all places of \(K(y)\) except for those which lie over some fixed finite set of places \(\Sigma_f\) of \(K\), with \(\Sigma_f\) depending only on \(f\). This generalizes a theorem of S. Beckmann [J. Reine Angew. Math. 419, 27-53 (1991; Zbl 0721.11052)] who considered geometrically connected, generically Galois covers of \(\mathbb P^1_K\), with \(K\) a number field.