Automorphisms of Twisted Chevalley Groups of type ${}^2{D}_{\mathrm{\ell }}(\mathrm{\ell }\ge 4)$ over Local Rings

We prove that all automorphisms of twisted Chevalley groups of type ${}^2{D}_{\mathrm{\ell }}$, $\mathrm{\ell }\ge 4$, and their elementary subgroups over commutative local rings with $1\mathrm{/}2$ are standard. More precisely, for elementary groups, every automorphism is a composition of strictly inner, diagonal, and ring automorphisms; for full groups, a central factor may also occur. In the adjoint case, diagonal automorphisms are strictly inner and the centre is trivial, so only strictly inner and ring factors are needed for both the elementary and full groups.