On the Arakelov theory of arithmetic surfaces (3/4)
par
Prof.Christophe SOULÉ(IHES)
→
Europe/Paris
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
IHES
Le Bois-Marie
35, route de Chartres
91440 Bures-sur-Yvette
Description
Let X be a semi-stable arithmetic surface of genus at least two and 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).