  Over a commutative noetherian ring $R$ of finite Krull dimension, we show
that every complex of flat cotorsion $R$-modules decomposes as a direct sum of
a minimal complex and a contractible complex. Moreover, we define the notion of
a semi-flat-cotorsion complex as a special type of semi-flat complex, and
provide functorial ways to construct a quasi-isomorphism from a semi-flat
complex to a semi-flat-cotorsion complex. Consequently, every $R$-complex can
be replaced by a minimal semi-flat-cotorsion complex in the derived category
over $R$. Furthermore, we describe structure of semi-flat-cotorsion
replacements, by which we recover classic theorems for finitistic dimensions.
In addition, we improve some results on cosupport and give a cautionary
example. We also explain that semi-flat-cotorsion replacements always exist and
can be used to describe the derived category over any associative ring.
