论文标题
广义雅各布人的模块化曲线和néron模型
Modular curves and Néron models of generalized Jacobians
论文作者
论文摘要
让$ x $成为离散估值环$ r $的场地上的平稳几何连接的投影曲线，而$ x $ $ x $的模量为$ x $，由$ x $的封闭式$ x $给出。相对于$ \ mathfrak {m} $，广义的jacobian $ j_ \ mathfrak {m} $ of $ x $是$ \ mathfrak {m} $，然后是torus的$ x $的jacobian的扩展。我们将其Néron模型以及特殊纤维的特征和组件组以及$ r $ $ x $的常规型号进行了描述。这概括了Raynaud对通常的Jacobian的著名描述。我们还为模块化曲线的通用雅各布人提供了一些计算，$ x_0（n）$在cusps上支持的模量。
Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$, and $\mathfrak{m}$ a modulus on $X$, given by a closed subscheme of $X$ which is geometrically reduced. The generalized Jacobian $J_\mathfrak{m}$ of $X$ with respect to $\mathfrak{m}$ is then an extension of the Jacobian of $X$ by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular model of $X$ over $R$. This generalizes Raynaud's well-known description for the usual Jacobian. We also give some computations for generalized Jacobians of modular curves $X_0(N)$ with moduli supported on the cusps.
