p-adic families of Siegel modular cuspforms

被引：36

作者：

Andreatta, Fabrizio ^{[1
]}

Iovita, Adrian ^{[2
,3
]}

Pilloni, Vincent ^{[4
]}

机构：

[1] Univ Statale Milano, Milan, Italy

[2] Concordia Univ, Montreal, PQ, Canada

[3] Univ Padua, Padua, Italy

[4] CNRS, Ecole Normale Super, Charge Rech Math, Lyon, France

来源：

ANNALS OF MATHEMATICS | 2015年 / 181卷 / 02期

关键词：

FORMS; REPRESENTATIONS; FILTRATION; VARIETIES; SHEAVES;

D O I：

10.4007/annals.2015.181.2.5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be an odd prime and g >= 2 an integer. We prove that a finite slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional weight space. The proof of this theorem relies on the construction of a family of sheaves of locally analytic overconvergent modular forms.

引用

页码：623 / 697

页数：75

共 42 条

[11]

Arthur J, 2004, CONTRIBUTIONS TO AUTOMORPHIC FORMS, GEOMETRY, AND NUMBER THEORY, P65

[12] p-adic modular forms of non-integral weight over Shimura curves [J].