Non-Archimedean entire curves in projective varieties dominating an elliptic curve
Jackson S. Morrow
备注：
The paper has been withdrawn by the author due to an error in the proof of Lemma 3.2. Section 1 up to Lemma 3.2 and Section 5 are to the best of the author's knowledge, still correct
设 K 是特征为零的代数闭、完备的非阿基米德赋值域。我们证明了不规则度为一的射影曲面的非阿基米德 Green–Griffiths–Lang 猜想。更确切地说，我们证明若 X/K 是无群的射影曲面，且允许到一条椭圆曲线的支配态射，则 X 是 K-解析 Brody 双曲的。证明的主要工具是一个定理，涉及允许支配态射到椭圆曲线的射影伪无群簇中非阿基米德整曲线的代数退化。
英文摘要：
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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