$mathcal P$-adic modular forms over Shimura curves over totally real fields
$mathcal P$-adic modular forms over Shimura curves over totally real fields
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$mathcal P$-adic 模形式在完全实数域上的 Shimura 曲线上
DOI：
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发表时间：
2004
影响因子：
1.8
通讯作者：
Payman L. Kassaei
中科院分区：
文献类型：
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作者：
Payman L. Kassaei
建立了一类酉PEL-Shimura曲线M‘K’上的$数学P~-进模型的基本理论。对于任何由M‘K’分类的不太‘超奇异’的PEL交换方案，我们构造了一个典范子群，它本质上是Frobenius核从特征p的提升.利用这种构造，我们定义了U和Frob算子.在Coleman的基础上，我们研究了U在超收敛的数学型P-进模型族上的作用的谱理论，证明了在给定的斜率下，U的超收敛特征形式的维度是权的局部常数函数。
We set up the basic theory of $mathcal P$-adic modular forms over certain unitary PEL Shimura curves M′K′. For any PEL abelian scheme classified by M′K′, which is not ‘too supersingular’, we construct a canonical subgroup which is essentially a lifting of the kernel of Frobenius from characteristic p. Using this construction we define the U and Frob operators in this context. Following Coleman, we study the spectral theory of the action of U on families of overconvergent $mathcal P$-adic modular forms and prove that the dimension of overconvergent eigenforms of U of a given slope is a locally constant function of the weight.