  The Hom closed colocalizing subcategories of the stable module category of a
finite group are classified. Along the way, the colocalizing subcategories of
the homotopy category of injectives over an exterior algebra, and the derived
category of a formal commutative differential graded algebra, are classified.
To this end, and with an eye towards future applications, a notion of local
homology and cosupport for triangulated categories is developed, building on
earlier work of the authors on local cohomology and support.
