  A theorem of Lurie and Pridham establishes a correspondence between formal
moduli problems and differential graded Lie algebras in characteristic zero,
thereby formalising a well-known principle in deformation theory. We introduce
a variant of differential graded Lie algebras, called partition Lie algebras,
in arbitrary characteristic. We then explicitly compute the homotopy groups of
free algebras, which parametrise operations. Finally, we prove generalisations
of the Lurie-Pridham correspondence classifying formal moduli problems via
partition Lie algebras over an arbitrary field, as well as over a complete
local base.
