17:00
Globally valued fields, adelic curves and Siu inequality
Abstract
In this talk, I will introduce the frameworks of globally valued fields (Ben Yaacov-Hrushovski) and adelic curves (Chen-Moriwaki). Both of these frameworks aim at understanding the arithmetic of fields sharing common features with global fields. A lot of examples fit in this scope (e.g. global fields, finitely generated extension of the prime fields, fields of meromorphic functions) and we will try to describe some of them.
Although globally valued fields and adelic curves came from different motivations and might seem quite different, they are related (and even essentially equivalent). This relation opens the door for new methods in the study of global arithmetic. As an application, we will sketch the proof of an arithmetic analogue of Siu inequality in algebraic geometry (a fundamental tool to detect the existence of global sections of line bundles in birational geometry). This is a joint work with Michał Szachniewicz.