Calculus on the moduli space of curves

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

Around the beginning of 1983, Gerd Faltings submitted a preprint called “Calculus on arithmetic surfaces” for publication. As he writes in the introduction of the published version, the ideas developed in the paper turned out to be “extremely useful” to the author in his proof, about five months later, of the Mordell conjecture.

According to its MathSciNet review, “[…] this paper has put arithmetic algebraic geometry on its feet, at least for curves.” In this colloquium style talk, which is held 40 years after its initial submission and at the occasion of the author’s retirement from the MPIM, we revisit and celebrate Gerd Faltings’ “Calculus” paper and discuss some recent developments related to its contents.