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Cours de l'IHES­­ 2016-2017

On the Arakelov theory of arithmetic surfaces (4/4)

by Prof. Christophe SOULÉ (IHES)

mercredi 22 mars 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

Let X be a semi-stable arithmetic surface of  genus at least two and $\omega$  the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and Moret-Bailly have conjectured an upper bound for the arithmetic self-intersection of $\omega$. They proved that a weak form of the abc conjecture follows from this inequality. We shall discuss a way of making their conjecture more precise in order that it implies the full abc conjecture (a  proof of which has been announced by Mochizuki).

Organisé par Emmanuel Ullmo
Contact Email: cecile@ihes.fr