ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS
ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS
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DOI：
10.1017/s147474802200010x
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发表时间：
2016-01
影响因子：
0.9
通讯作者：
Shin Hattori
中科院分区：
文献类型：
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作者：
Shin Hattori
设p是一个有理素数.设F是一个全真实的数域，使得F在p上是非分歧的，且F的任何素理想除p的剩余度都是$\leq 2$。本文证明了由Andreatta，Iovita，和Pilloni构造的$\mathrm {Res}_{F/\mathbb {Q}}（\mathit {GL}_{2}）$的特征簇在整数权下是恰当的.我们还证明了一个较弱的结果$p=2$。
Abstract Let p be a rational prime. Let F be a totally real number field such that F is unramified over p and the residue degree of any prime ideal of F dividing p is $\leq 2$ . In this paper, we show that the eigenvariety for $\mathrm {Res}_{F/\mathbb {Q}}(\mathit {GL}_{2})$ , constructed by Andreatta, Iovita, and Pilloni, is proper at integral weights for $p\geq 3$ . We also prove a weaker result for $p=2$ .