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SÉMINAIRE DES THÉSARDS

de l’Institut de mathématiques de Jussieu - Paris Rive Gauche

par des doctorants — pour des non-spécialistes

Mercredi 20 février 2019 à 18 h 00 Sophie Germain, salle 2015

Mathieu Dutour (IMJ-PRG)

A Deligne-Riemann-Roch isometry for modular curves

In 1987, Deligne proved a type of Riemann-Roch theorem, which aims to relate geometric and arithmetic properties, for compact Riemann surfaces endowed with smooth hermitian metrics.

When trying to apply this result to the case of modular curves, we find that there is a crucial hypothesis that is not satisfied : the Poincaré metric does not behave nicely, and has singularities at some points.

The purpose of this talk is to present a method, called analytic surgery, which we can use to avoid these singularities, and get a variation of Deligne’s results. Some unexpected applications stem from these considerations, such as explicit values of some derivatives of Selberg zeta functions.

Organisateurs :

A.Bengus-Lasnier, E.Di Nezza, I.Ftouhi, M.Gonçalves Lamas, L.Liu, R. Petrides

Détails et archives : webusers.imj-prg.fr/~mario.goncalves-lamas/sdt

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