Local Cohomology and Serre Class in Derived Category D(R)

Let [Formula: see text] be a Serre class of the category of modules and [Formula: see text] an ideal of a commutative noetherian ring [Formula: see text]. Generalizations of depth and cohomological dimension with respect to [Formula: see text]for complexes are given. Some characterizations of these notions in terms of RHom, Koszul cohomology and local cohomology are found. The membership of the local cohomology [Formula: see text] of an [Formula: see text]-complex [Formula: see text] in [Formula: see text] is studied from below ([Formula: see text]) and from above ([Formula: see text]), which in special cases recovers and generalizes the known results about the usual depth and cohomological dimension of modules.