论文标题
特征p的希尔伯特模块化形式的几何体重移动算子
Geometric weight-shifting operators on Hilbert modular forms in characteristic p
论文作者
论文摘要
我们对Hilbert Modular Forms的特征性$ P $进行了彻底的研究，对作者与Sasaki的先前工作概括为$ P $在完全真实的现实领域$ f $中损坏的情况。特别是，我们使用Reduzzi和Xiao定义的部分Hasse不变性和Kodaira-Spencer过滤来改善Andreatta和Goren的构造部分$θ$ operator，从而获得了对重量的影响，从几何学的角度来看，其对重量的影响是最佳的。此外，我们用几何构造的部分Frobenius操作员来描述部分$θ$ - 操作员的内核。最后，我们应用结果来证明Mod $ P $ Hilbert模块化形式的最小权重的部分阳性结果。
We carry out a thorough study of weight-shifting operators on Hilbert modular forms in characteristic $p$, generalizing the author's prior work with Sasaki to the case where $p$ is ramified in the totally real field $F$. In particular we use the partial Hasse invariants and Kodaira-Spencer filtrations defined by Reduzzi and Xiao to improve on Andreatta and Goren's construction of partial $Θ$-operators, obtaining ones whose effect on weights is optimal from the point of view of geometric Serre weight conjectures. Furthermore we describe the kernels of partial $Θ$-operators in terms of images of geometrically constructed partial Frobenius operators. Finally we apply our results to prove a partial positivity result for minimal weights of mod $p$ Hilbert modular forms.
