Genus of abstract modular curves with level l structure

Genus of abstract modular curves with level l structure

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Anna Cadoret , IAS/Ecole Polytechnique
IAS Room S-101

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 infty with l. I will sketch a purely algebraic proof of the growth of the genus - working in particular in positive characteristic.