  For a left coherent ring A with every left ideal having a countable set of
generators, we show that the coderived category of left A-modules is compactly
generated by the bounded derived category of finitely presented left A-modules
(reproducing a particular case of a recent result of Stovicek with our
methods). Furthermore, we present the definition of a dualizing complex of
fp-injective modules over a pair of noncommutative coherent rings A and B, and
construct an equivalence between the coderived category of A-modules and the
contraderived category of B-modules. Finally, we define the notion of a
relative dualizing complex of bimodules for a pair of noncommutative ring
homomorphisms A \to R and B \to S, and obtain an equivalence between the
R/A-semicoderived category of R-modules and the S/B-semicontraderived category
of S-modules. For a homomorphism of commutative rings A\to R, we also construct
a tensor structure on the R/A-semicoderived category of R-modules. A vision of
semi-infinite algebraic geometry is discussed in the introduction.
