  An important result in tilting theory states that a class of modules over a
ring is a tilting class if and only if it is the Ext-orthogonal class to a set
of compact modules of bounded projective dimension. Moreover, cotilting classes
are precisely the resolving and definable subcategories of the module category
whose Ext-orthogonal class has bounded injective dimension.
  In this article, we prove a derived counterpart of the statements above in
the context of silting theory. Silting and cosilting complexes in the derived
category of a ring generalise tilting and cotilting modules. They give rise to
subcategories of the derived category, called silting and cosilting classes,
which are part of both a t-structure and a co-t-structure. We characterise
these subcategories: silting classes are precisely those which are intermediate
and Ext-orthogonal classes to a set of compact objects, and cosilting classes
are precisely the cosuspended, definable and co-intermediate subcategories of
the derived category.
