Generalizations of Siegel’s and Picard’s theorems


We prove new theorems that are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. These include results on integral points over varying number fields of bounded degree and results on Kobayashi hyperbolicity. We give a number of new conjectures describing, from our point of view, how we expect Siegel’s and Picard’s theorems to optimally generalize to higher dimensions.


Aaron Levin

Centro di Ricerca Matematica Ennio De Giorgi
Scuola Normale Superiore
56100 Pisa