Shafarevich morphism for linear representations in positive characteristic and hyperbolicity

Date/heure
16 October 2023
14:00 - 15:00

Lieu
Salle de conférences Nancy

Oratrice ou orateur
Ya Deng

Catégorie d'évènement
Séminaire de géométrie complexe

The Shafarevich conjecture predicts the holomorphic convexity of complex projective varieties. It results in the existence of the Shafarevich morphism. In the last three decades, this conjecture has been extensively studied when considering cases where fundamental groups are subgroups of complex general linear groups. In this talk I will discuss some recent work on the construction of Shafarevich morphism for any linear representation $\rho :{\pi }_1(X)\to G{L}_N(K)$ where $X$ is any complex quasi-projective variety and $K$ is any field of positive characteristic. I will also explain the proof of the generalized Green-Griffiths-Lang conjecture for $X$ when $\rho$ is a big representation. This talk is based on a joint work with Yamanoi.