On the Arakelov theory of arithmetic surfaces (4/4)
by Prof. Christophe SOULÉ (IHES)
at IHES ( Amphithéâtre Léon Motchane )
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|