  We investigate the competition between the electron-vibron interaction
(interaction with the Jahn-Teller phonons) and the Coulomb repulsion in a
system with the local pairing of electrons on the 3-fold degenerate lowest
unoccupied molecular orbital (LUMO). The el.-vib. interaction and the local
pairing radically change conductivity and magnetic properties of alkali-doped
fullerides $\texttt{A}_{n}\texttt{C}_{60}$, which would have to be
antiferromagnetic Mott insulators: we have shown that materials with $n=1,5$
and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors but not superconductors;
$n=3$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors and
superconductors at low temperatures, but with $\texttt{A}=\texttt{Cs}$ they are
Mott-Jahn-Teller insulators at normal pressure; $n=2,4$ are nonmagnetic Mott
insulators. Thus superconductivity, conductivity and insulation of these
materials have common nature. Using this approach we obtain the phase diagram
of $\texttt{A}_{3}\texttt{C}_{60}$ analytically, which is the result of
interplay between the local pairing, the el.-vib. interaction, Coulomb
correlations, and formation of small radius polarons.
