We prove vanishing results for the coherent cohomology of the good reduction modulo $p$ of the Siegel modular variety with coefficients in some automorphic bundles. We show that for an automorphic bundle with highest weight $\lambda$ near the walls of the antidominant Weyl chamber, there is an integer $e\ge 0$ such that the cohomology is concentrated in degrees $[0,e]$. The accessible weights with our method are not necessarily regular and not necessarily $p$-small. Since our method is technical, we also provide an algorithm written in SageMath that computes explicitly the vanishing results.

中文翻译：

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正特征中 Siegel 变种上自守向量束的相干同源性的消失结果

我们 $p$ 寻找了 Siegel 模变体的良好归约模 $p$ 量与一些自守束中的系数的相干同源性的消失结果。我们表明，对于在反优势 Weyl 室壁附近具有最高权重 $\lambda$ 的自守束，存在一个整数， $e\ge 0$ 使得同源性集中在度 $[0,e]$ 中。我们的方法可访问的权重不一定是规则的，也不一定是 p-small。由于我们的方法是技术性的，我们还提供了一个用 SageMath 编写的算法，用于显式计算消失的结果。