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Séminaire de Théorie Algorithmique des Nombres

Modular Galois representations p-adically using Makdisi's moduli-friendly forms

Nicolas Mascot

( Trinity College Dublin )

Online

le 22 septembre 2020 à 10:00

We will present a p-adic method to compute Galois representations attached to modular forms. This method compares very favourably to the better-known complex-analytic approach. The main ingredient is the use of “moduli-friendly" forms introduced by Makdisi, which allow us to evaluate modular forms at p-adic points of modular curves, and thus to compute in the Jacobian of modular curves without writing down any equations nor q-expansions.