论文标题
mod $ p $自动形态和部分哈斯的权重
Weights of mod $p$ automorphic forms and partial Hasse invariants
论文作者
论文摘要
对于赋予配置器$μ$的有限字段的连接，还原的集团$ g $，我们将$（g，μ）$的Zip圆锥定义为$ g $ zips的堆栈上所有可能的Mod $ p $自动形态形式的圆锥。该圆锥体的猜想与特征性$ p $ p $自动形式的重量相吻合，用于hodge型shimura的良好减少品种。我们完全证明了特征性$ 0 $自动形式的重量锥包含Zip锥中，这为该猜想提供了进一步的证据。此外，我们确切确定何时由部分Hasse不变性的权重产生，这是钻石和金林（Kassaei）和Goldring-koskivirta的群体理论概括。
For a connected, reductive group $G$ over a finite field endowed with a cocharacter $μ$, we define the zip cone of $(G,μ)$ as the cone of all possible weights of mod $p$ automorphic forms on the stack of $G$-zips. This cone is conjectured to coincide with the cone of weights of characteristic $p$ automorphic forms for Hodge-type Shimura varieties of good reduction. We prove in full generality that the cone of weights of characteristic $0$ automorphic forms is contained in the zip cone, which gives further evidence to this conjecture. Furthermore, we determine exactly when the zip cone is generated by the weights of partial Hasse invariants, which is a group-theoretical generalization of a result of Diamond--Kassaei and Goldring--Koskivirta.
