Nearly ordinary rank four Galois representations and $p$-adic Siegel modular forms
Nearly ordinary rank four Galois representations and $p$-adic Siegel modular forms
复制标题
几乎普通的四阶伽罗瓦表示和 $p$-adic Siegel 模形式
DOI：
10.1112/s0010437x06002119
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发表时间：
2006
影响因子：
1.8
通讯作者：
J. Tilouine
中科院分区：
文献类型：
--
作者：
J. Tilouine
本文致力于证明两个结果。第一个结果是作者在1994年提出的猜想。它涉及在某些假设下，$p$-近平凡伽罗瓦表示的泛形变环与希达意义下的泛近平凡赫克代数的一个局部分支的一致性。另一个结果依赖于第一个结果，它涉及某些阿贝尔曲面的模性。更确切地说，可以将某些定义在有理数域上的不可约阿贝尔曲面与过收敛的$p$-进尖点本征形式相关联。本文没有研究这些形式是否是经典的这一问题。
This paper is devoted to the proof of two results. The first was conjectured in 1994 by the author. It concerns the identity, under certain assumptions, of the universal deformation ring of $p$-nearly ordinary Galois representations and a local component of the universal nearly ordinary Hecke algebra in the sense of Hida. The other, which relies on the first, concerns the modularity of certain abelian surfaces. More precisely, one can associate to certain irreducible abelian surfaces defined over the rationals overconvergent $p$-adic cusp eigenforms. The question of whether these forms are classical is not studied in this paper.