Explicit Serre duality on complex spaces

In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof, of Serre duality on any reduced pure n-dimensional paracompact complex space X. At the core of the paper is the introduction of certain fine sheaves BXn,q of currents on X of bidegree (n,q), such that the Dolbeault complex (BXn,•,∂¯) becomes, in a certain sense, a dualizing complex. In particular, if X is Cohen-Macaulay then (BXn,•,∂¯) is an explicit fine resolution of the Grothendieck dualizing sheaf.