Cours de l'IHES­­ 2016-2017

On the Arakelov theory of arithmetic surfaces (1/4)

by Prof. Christophe SOULÉ (IHES)

Amphithéâtre Léon Motchane (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).

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