论文标题
整个theta运营商未受到素数
Entire theta operators at unramified primes
论文作者
论文摘要
从Serre，Katz和Swinnerton-Dyer的作品开始，Theta运营商在研究$ p $ - adiC和$ \ bmod p $模块化表单和Galois表示的研究中发挥了关键作用。本文在pel型shimura品种上以theta运营商的自同形形式取得了两个主要结果：1）$ \ bmod p $ $ p $ p $ p $ p $ - adic-shimaS-shimaS-shimura运营商的分析延续，以均未造成的质量p $ $ p $ p $ p $ - 没有出现的新的$ \ bmod p $ theta运营商作为$ \ bmod p $减少maass-shimura运营商。尽管本文的主要成就涉及Shimura品种的几何形状以及对差异操作员的后果，但我们以对Galois表示的应用结论。我们的方法涉及对Shimura品种的行为进行仔细的分析，并使我们能够获得比先前技术所允许的更多的一般结果，包括用于任意程度的CM领域中的任意签名，矢量权重和未受到的素数。
Starting with work of Serre, Katz, and Swinnerton-Dyer, theta operators have played a key role in the study of $p$-adic and $\bmod p$ modular forms and Galois representations. This paper achieves two main results for theta operators on automorphic forms on PEL-type Shimura varieties: 1) the analytic continuation at unramified primes $p$ to the whole Shimura variety of the $\bmod p$ reduction of $p$-adic Maass--Shimura operators {\it a priori} defined only over the $μ$-ordinary locus, and 2) the construction of new $\bmod p$ theta operators that do not arise as the $\bmod p$ reduction of Maass--Shimura operators. While the main accomplishments of this paper concern the geometry of Shimura varieties and consequences for differential operators, we conclude with applications to Galois representations. Our approach involves a careful analysis of the behavior of Shimura varieties and enables us to obtain more general results than allowed by prior techniques, including for arbitrary signature, vector weights, and unramified primes in CM fields of arbitrary degree.
