  We show that up to potential isogeny, there are only finitely many abelian
varieties of dimension $d$ defined over a number field $K$, such that for any
finite place $v$ outside a fixed finite set $S$ of places of $K$ containing the
archimedean places, it has either good reduction at $v$, or totally bad
reduction at $v$ and good reduction over a quadratic extension of the
completion of $K$ at $v$.
