论文标题
统一shimura品种的广义theta运营商
Generalised theta operators on unitary Shimura varieties
论文作者
论文摘要
本文的主要结果是建造了新的重量转移操作员，类似于Arxiv的Theta操作员：1902.10911，Arxiv：1712.06969等，在较低的Ekedahl-Oort阶层中定义了单一的shimura priepties $（$ and）的$（N-1）$（N-1）的几何特殊纤维的$（ $ e $，我们认为这是二次假想。这些操作员对某些分级带轮作用，这些系带是从EO层的算术结构中获得的，尤其是每个层上的$ p $ lank。我们希望这些操作员能够将模块化形式的Hecke-eigensystems的研究应用于Modulo $ p $的Hecke-eigensystems和Serre猜想的重量部分的概括。
The main result of this paper is the construction of a new class of weight shifting operators, similar to the theta operators of arXiv:1902.10911, arXiv:1712.06969 and others, which are defined on the lower Ekedahl-Oort strata of the geometric special fibre of unitary Shimura varieties of signature $(n-1, 1)$ at a good prime $p$, split in the in the reflex field $E$, which we assume to be quadratic imaginary. These operators act on certain graded sheaves which are obtained from the arithmetic structure of the EO strata, in particular the $p$-rank on each stratum. We expect these operators to have applications to the study of Hecke-eigensystems of modular forms modulo $p$ and generalisations of the weight part of Serre's conjecture.
