论文标题
小组环的希尔伯特模块化形式
Group Ring Valued Hilbert Modular Forms
论文作者
论文摘要
在本文中，我们研究了钻石操作员对Hilbert模块化形式的作用，并在一般的交换环中具有系数。特别是，我们概括了柴的结果，即希尔伯特模块化形式的恒定术语图与Nebentypus的溢流性，以设置群环值模块化形式。作为一种应用，我们构建了Dasgupta-kakde在奇数上构思的某些希尔伯特模块化形式。 Since the forms required for the Brumer-Stark conjecture live on the non-PEL Shimura variety associated to the reductive group $G = Res_{F/Q}(GL_2)$, as opposed to the PEL Shimura variety associated to the subgroup $G^* \subset G$ studied by Chai, we give a detailed explanation of theory of algebraic diamond operators for $G$, as well as how the theory of $ g $的环形和最小压实可以从$ g^*$的类似理论中得出。
In this paper, we study the action of diamond operators on Hilbert modular forms with coefficients in a general commutative ring. In particular, we generalize a result of Chai on the surjectivity of the constant term map for Hilbert modular forms with nebentypus to the setting of group ring valued modular forms. As an application, we construct certain Hilbert modular forms required for Dasgupta-Kakde's proof of the Brumer-Stark conjecture at odd primes. Since the forms required for the Brumer-Stark conjecture live on the non-PEL Shimura variety associated to the reductive group $G = Res_{F/Q}(GL_2)$, as opposed to the PEL Shimura variety associated to the subgroup $G^* \subset G$ studied by Chai, we give a detailed explanation of theory of algebraic diamond operators for $G$, as well as how the theory of toroidal and minimal compactifications for $G$ may be deduced from the analogous theory for $G^*$.
