Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result

We discuss two results about projective representations of fundamental groups of quasiprojective varieties. The first is a realization result that, under a nonresonance assumption, allows us to realize such representations as monodromy representations of flat projective logarithmic connections. The second is a lifting result: any representation as above, after restriction to a Zariski open set and finite pull-back, can be lifted to a linear representation. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.