Genus of abstract modular curves with level ℓℓ structure - Ana Cadoret

Ana Cadoret Ecole Polytechnique; Member, School of Mathematics November 21, 2013 To any bounded family of 𝔽ℓFℓ-linear representations of the etale fundamental of a curve XX one can associate families of abstract modular curves which, in this setting, generalize the `usual' modular curves with level ℓℓ structure. Under mild hypotheses, it is expected that the genus (and even the geometric gonality) of these curves goes to ∞∞ with ℓℓ. I will sketch a purely algebraic proof of the growth of the genus - working in particular in positive characteristic. For more videos, visit http://video.ias.edu