What is Arakelov Geometry?

20 June 2019
16:00
Esteban Gomezllata Marmolejo
Abstract

Arakelov geometry studies schemes X over ℤ, together with the Hermitian complex geometry of X(ℂ).
Most notably, it has been used to give a proof of Mordell's conjecture (Faltings's Theorem) by Paul Vojta; curves of genus greater than 1 have at most finitely many rational points.
In this talk, we'll introduce some of the ideas behind Arakelov theory, and show how many results in Araklev theory are analogous—with additional structure—to classic results such as intersection theory and Riemann Roch.

  • Junior Geometry and Topology Seminar