论文标题
曲线雅各布人的模型
Models of Jacobians of curves
论文作者
论文摘要
我们表明，雅各比人的雅各布曲线在环形品种上总是允许néron模型。这些模型很少是准紧凑或分离的，但是我们还对这种雅各布人的准混合分离组模型进行了完整的分类。特别是，我们显示了最大准紧凑分离的组模型的存在，我们称之为饱和模型，该模型具有所有扭转部分的扩展属性。 Néron模型和饱和模型在Dedekind基础上重合，因此饱和模型对Néron模型的经典概念进行了替代的概括，以对较高维度的基础。在一般情况下，我们为Néron模型和饱和模型提供了必要的条件。大多数其他人都会下降的关键结果是\ cite {molcho2018 The-logarithmic}的对数Jacobian是Jacobian的log Neron模型。
We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete classification of quasi-compact separated group-models of such Jacobians. In particular we show the existence of a maximal quasi-compact separated group model, which we call the saturated model, which has the extension property for all torsion sections. The Néron model and the saturated model coincide over a Dedekind base, so the saturated model gives an alternative generalisation of the classical notion of Néron models to higher-dimensional bases; in the general case we give necessary and sufficient conditions for the Néron model and saturated model to coincide. The key result, from which most others descend, is that the logarithmic Jacobian of \cite{Molcho2018The-logarithmic} is a log Neron model of the Jacobian.
