论文标题
通过特征$ p $的汽车形式的griffiths-schmid条件
Griffiths-Schmid conditions for automorphic forms via characteristic $p$
论文作者
论文摘要
我们为特征$ 0 $和特征$ p $的自动形式空间的空间建立了消失的结果。我们证明，对于Hodge型Shimura品种，特征性的任何非零自动形式的重量$ 0 $都满足了Griffiths-Schmid条件，纯粹是代数，特征$ P $方法。我们陈述了一般霍奇型Shimura品种的猜想，内容涉及在体重上以特征性$ p $中的自动形式的消失。我们在分裂素数中验证了统一的pel shimura品种（n-1,1）$的统一构想。
We establish vanishing results for spaces of automorphic forms in characteristic $0$ and characteristic $p$. We prove that for Hodge-type Shimura varieties, the weight of any nonzero automorphic form in characteristic $0$ satisfies the Griffiths-Schmid conditions, by purely algebraic, characteristic $p$ methods. We state a conjecture for general Hodge-type Shimura varieties regarding the vanishing of the space of automorphic forms in characteristic $p$ in terms of the weight. We verify this conjecture for unitary PEL Shimura varieties of signature $(n-1,1)$ at a split prime.
