论文标题
$ p $ - hodge类型Shimura品种的模块化形式的家族与非空位
$p$-adic families of modular forms for Hodge type Shimura varieties with non-empty ordinary locus
论文作者
论文摘要
我们概括了Andreatta，Iovita和Pilloni的一些结果，以及作者的hodge型Shimura品种，具有非空位的普通基因座。对于任何$ p $ - 亚种的重量$κ$，我们在捆绑部分中给出了过度融合模块化$κ$的几何定义。我们表明，我们的滑轮生活在分析家庭中，为整体重量的经典滑轮插值。我们定义了Hecke代数的动作，其中包括$ p $的完全连续的操作员。在某些简单的情况下，我们还构建了特征因素。
We generalize some of the results of Andreatta, Iovita, and Pilloni and the author to Hodge type Shimura varieties having non-empty ordinary locus. For any $p$-adic weight $κ$, we give a geometric definition of the space of overconvergent modular forms of weight $κ$ in terms of sections of a sheaf. We show that our sheaves live in analytic families, interpolating the classical sheaves for integral weights. We define an action of the Hecke algebra, including a completely continuous operator at $p$. In some simple cases, we also build the eigenvariety.
