On the Gersten–Witt complex of an Azumaya algebra with involution

Let (A,σ) be an Azumaya algebra with involution over a regular ring R. We prove that the Gersten–Witt complex of defined by Gille is isomorphic to Bayer-Fluckiger, Parimala and author. Advantages both constructions are used show exact when dim⁡R≤3, indA≤2 σ orthogonal or symplectic. This means Grothendieck–Serre conjecture holds for group R-scheme σ-unitary elements in A under same hypotheses; R not required contain field.