Non-Archimedean entire curves in projective varieties dominating an elliptic curve

2020/05/25 by Morrow, Jackson S.
#(32P05) #32Q45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.12353

Abstract

Let K be an algebraically closed, complete, non-Archimedean valued field of characteristic zero. We prove the non-Archimedean Green--Griffiths--Lang conjecture for projective surfaces of irregularity one. More precisely, we prove that if X/K is a groupless, projective surface that admits a dominant morphism an elliptic curve, then X is K-analytically Brody hyperbolic. The main ingredient in our proof is a theorem concerning the algebraic degeneracy of non-Archimedean entire curves in projective, pseudo-groupless varieties admitting a dominant morphism to an elliptic curve.

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