  This paper is concerned with an interpretation of f-cohomology, a
modification of motivic cohomology of motives over number fields, in terms of
motives over number rings. Under standard assumptions on mixed motives over
finite fields, number fields and number rings, we show that the two extant
definitions of f-cohomology of mixed motives $M_\eta$ over F--one via
ramification conditions on $\ell$-adic realizations, another one via the
K-theory of proper regular models--both agree with motivic cohomology of
$\eta_{!*} M_\eta[1]$. Here $\eta_{!*}$ is constructed by a limiting process in
terms of intermediate extension functors $j_{!*}$ defined in analogy to
perverse sheaves.
