This paper deals with the determination of the nilpotent classes in the Lie algebra \({\mathfrak g}\) of a reductive algebraic group G defined over an algebraically closed field k in one of the few cases where it was not yet known: G of type \(F_ 4\), \(char(k)=2\). In this case there are 22 nilpotent orbits (and 26 over a finite field). The structure of the stabilizers (dimension, group of components, type of the reductive part of the identity component) is also described, as well as the order relation by inclusion of Zariski closures and the Springer correspondence with representations of the Weyl group. There are also some results on the sheets in \({\mathfrak g}\). The basic tool is a systematic use of the commutation formulae.
[Since this paper was written, D. F. Holt and the author have worked out the remaining cases (”Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic”, to appear in J. Aust. Math. Soc.); the method used there gives less information, and in the case of \(F_ 4\), \(char(k)=2\), would require some modification to handle the class \(\tilde A_ 2+A_ 1.]\)