  Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an
algebraically closed field of characteristic 2. We construct a Springer
correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie
algebras in characteristic 2, the structure of component groups of nilpotent
centralizers is determined and the number of nilpotent orbits over finite
fields is obtained.
