The present invention pertains to a process for the manufacture of a grafted fluorinated polymer comprising at least one grafted side chain comprising one or more glycosidic recurring units [polymer (F)], said process comprising polymerizing: vinylidene fluoride (VDF), optionally, one or more other fluorinated monomers [monomers (F)], and optionally, one or more (meth)acrylic monomers [monomers (MA)], in the presence of at least one polysaccharide derivative [derivative (P)], said polysaccharide derivative having a dynamic viscosity of less than 15 mPa×s, as measured according to ASTM D445 at 20° C. in an aqueous solution at a concentration of 2% by weight, and by further providing novel polymers (F) as defined above.