To any bounded family of F_l linear representations of the etale fundamental of a curve X one can associate families of abstract modular curves which, in this setting, generalize the ´usual´ modular curves with level l structure Y_0(l), Y_1(l), Y(l) etc. Under mild hypotheses, it is expected that the genus -and even the geometric gonality- of these curves goes to infinity with l. I will sketch a purely algebraic proof of the growth of the genus - working in particular in positive characteristic.