论文标题
完美的模块化曲线的积分模型
An integral model of the perfectoid modular curve
论文作者
论文摘要
我们构建了完美的模块化曲线的积分模型。在研究这个对象时，我们证明了在完美素水平上相干的共同体学的一些消失结果。我们在有限级别使用局部二元定理来计算双重曲线的连贯的comomology。我们可以将结构捆扎的二元组合为结构上的捆绑，将完整的共同体学的双重性描述为重量$ 2 $和跟踪地图的整体风口尖的反向限制。
We construct an integral model of the perfectoid modular curve. Studying this object, we prove some vanishing results for the coherent cohomology at perfectoid level. We use a local duality theorem at finite level to compute duals for the coherent cohomology of the integral perfectoid curve. Specializing to the structural sheaf, we can describe the dual of the completed cohomology as the inverse limit of the integral cusp forms of weight $2$ and trace maps.
