Discriminants of orthogonal involutions on central simple algebras with tame gauges

In this article we generalize the results of Chacron et al. (1995) [4] concerning the computation of the discriminants of involutions of the first kind on central division algebras over Henselian valued fields of residue characteristic different from 2. We prove analogous results for orthogonal involutions on tame central simple algebras with simple residue algebras over a wide class of Henselian valued fields of arbitrary residue characteristic (see Corollary 2.18).