CRM: Centro De Giorgi
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Fundamental Groups in Arithmetic and Algebraic Geometry

Growth of the genus of abstract modular curves 'with level l structure' in positive characteristic

speaker: Anna Cadoret (Ecole Polytechnique, Palaiseau)

abstract: To any bounded family of \bar{\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 - from a moduli point of view - the `classical' modular curves with level l structure. Under mild hypotheses, it is expected that the genus (and even the geometric gonality) of these curves goes to infty with l. I will present an overview of the results about the genus (especially in positive char, where the situation is more difficult to handle) and, if time allows, give some hints about the proofs. (partly joint with Akio Tamagawa)

Thu 19 Dec, 11:15 - 12:15, Aula Dini
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