Let p be a rational prime and q a power of p. Let $\mathfrak{n}$ be a non-constant monic polynomial in ${\mathbb{F}}_q[t]$ which has a prime factor of degree prime to $q-1$. In this paper, we define a Drinfeld modular curve $Y_1^{\mathrm{\Delta }}(\mathfrak{n})$ over $A[1/\mathfrak{n}]$ and study the structure around cusps of its compactification $X_1^{\mathrm{\Delta }}(\mathfrak{n})$, in a parallel way to Katz-Mazur's work on classical modular curves. Using them, we also define a Hodge bundle over $X_1^{\mathrm{\Delta }}(\mathfrak{n})$ such that Drinfeld modular forms of level ${\mathrm{\Gamma }}_1(\mathfrak{n})$, weight k and some type are identified with global sections of its k-th tensor power.

中文翻译：

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关于阶Γ1Δ(n)的Drinfeld模曲线的紧化

设p为有理素数，q为p的幂。让$\mathfrak{n}$ 是一个非常量的单调多项式 ${\mathbb{F}}_q[吨]$ 其中有一个素数的素因数 $q-1$. 在本文中，我们定义了一条 Drinfeld 模曲线${是}_1^{\mathrm{\Delta }}(\mathfrak{n})$ 超过 $\mathrm{一种}[1/\mathfrak{n}]$ 并研究其密实化的尖端周围的结构 $X_1^{\mathrm{\Delta }}(\mathfrak{n})$，与 Katz-Mazur 在经典模曲线上的工作并行。使用它们，我们还定义了一个 Hodge bundle$X_1^{\mathrm{\Delta }}(\mathfrak{n})$ 使得 Drinfeld 模块化水平面形式 ${\mathrm{\Gamma }}_1(\mathfrak{n})$，权重k和某些类型用其第k个张量幂的全局部分标识。