论文标题
mod $ p $自动形式的分裂性和某些hodge型shimura品种的圆锥体构想
Divisibility of mod $p$ automorphic forms and the cone conjecture for certain Shimura varieties of Hodge-type
论文作者
论文摘要
对于几种hodge型shimura的特征性$ p $良好减少的品种，我们表明，汽车形式的重量是由$ g $ g $ zips的粉红色柔角 - Ziegler编码的。这建立了作者在先前论文中提出的一般猜想的几个实例。此外，在这些情况下，我们证明了重量位于体重空间特定区域的任何mod $ p $自动形式都可以由部分哈斯不变。这将概括为其他shimura品种的先前钻石 - 卡萨伊对希尔伯特模块化形式的结果。
For several Hodge-type Shimura varieties of good reduction in characteristic $p$, we show that the cone of weights of automorphic forms is encoded by the stack of $G$-zips of Pink-Wedhorn-Ziegler. This establishes several instances of a general conjecture formulated in previous papers by the authors. Furthermore, we prove in these cases that any mod $p$ automorphic form whose weight lies in a specific region of the weight space is divisible by a partial Hasse invariant. This generalizes to other Shimura varieties previous results of Diamond--Kassaei on Hilbert modular forms.
