论文标题
曲线模量空间的非架构双曲线
Non-archimedean hyperbolicity of the moduli space of curves
论文作者
论文摘要
让$ k $成为一个完全封闭的特征性零的代数封闭的非Archimedean有价值字段，让$ x $是$ k $的有限型方案。我们说，$ x $是$ k $ - 分析性的borelybolic，如果对于每种有限类型减少$ k $上的$ s $ s $ s $ s $，则来自刚性分析$ s^{\ mathrm {an}} $ $ s $ $ s $的每种刚性分析形态，$ s $使用Viehweg-Zuo结构和Cherry-Ru的$ k $ Analytix Big Picard Theorem，我们表明，对于$ n \ geq 3 $和$ g \ geq 2 $，精美的模量$ \ nathcal {m}^{m}^{n]} $ k $ - 分析borelytybolic。
Let $K$ be a complete algebraically closed non-archimedean valued field of characteristic zero, and let $X$ be a finite type scheme over $K$. We say $X$ is $K$-analytically Borel hyperbolic if, for every finite type reduced scheme $S$ over $K$, every rigid analytic morphism from the rigid analytification $S^{\mathrm{an}}$ of $S$ to the rigid analytification $X^{\mathrm{an}}$ of $X$ is algebraic. Using the Viehweg-Zuo construction and the $K$-analytic big Picard theorem of Cherry-Ru, we show that, for $N \geq 3$ and $g \geq 2$, the fine moduli space $\mathcal{M}^{[N]}_{g,K}$ over $K$ of genus $g$ curves with level $N$-structure is $K$-analytically Borel hyperbolic.
