Seminario Teoría de Números
Equidistribution of integers, potential theory and the essential minimum of Faltings` height
Ponente: Binggang QU (ICMAT)Fecha: lunes 03 de noviembre de 2025 - 12:30Lugar: Aula 420, Módulo 17, Departamento de Matemáticas, UAM
Resumen:
Let \(K \subseteq \mathbb{C}\) be a compact subset that is invariant under complex conjugation. We say an algebraic integer \(x\) is ``totally in \(K\)'', if we have \(O(x) \subseteq K\), where \(O(x)\) is the Galois orbit of \(x\). The classical Fekete-Szegö theorem characterized compact subsets that could have infinitely many algebraic integers totally in it. Very recently, there is a breakthrough by Smith-Orloski-Sardari that further characterized compactly supported probability measures on \(\mathbb{C}\) that could be properly approximated by Galois orbits of algebraic integers.
We shall give some remarks on the recent Smith-Orloski-Sardari equidistribution theorem, and also give an application that the essential minimum of Faltings' height of elliptic curves can be attained by those who have good reduction everywhere. This is based on an ongoing project joint with Jose Ignacio Burgos Gil, Ricardo Menares and Martín Sombra.
