On the Arakelov theory of arithmetic surfaces (3/4)

par Prof. Christophe SOULÉ (IHES)

mercredi 15 mars 2017, 10:30 → 12:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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).

Video https://youtu.be/MOZZbQSnO5g