Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.12353 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909493664677888 |
|---|---|
| author | Morrow, Jackson S. |
| author_facet | Morrow, Jackson S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_12353 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Non-Archimedean entire curves in projective varieties dominating an elliptic curve Morrow, Jackson S. Algebraic Geometry Number Theory 32Q45, (32P05) 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. |
| title | Non-Archimedean entire curves in projective varieties dominating an elliptic curve |
| topic | Algebraic Geometry Number Theory 32Q45, (32P05) |
| url | https://arxiv.org/abs/2005.12353 |