  We show that complex local systems with quasi-unipotent monodromy at infinity
over a normal complex variety are Zariski dense in their moduli. v2: we waited
for feedback and added a consequence of Alexandr Petrov's theorem. 3: we
tightened the last section. Final version: appears in Israel Journal of
Mathematics. footnote added to Conjecture 1.1: Aaron Landesman and Daniel Litt
just made available a preprint showing that there is a lower bound for the rank
of geometric local systems with infinite mon-odromy on certain curves, and
consequently the conjecture can not be true in this generality.
