Ordinary p-adic étale Cohomology Groups Attached to Towers of Elliptic Modular Curves
Ordinary p-adic étale Cohomology Groups Attached to Towers of Elliptic Modular Curves
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附属于椭圆模曲线塔的普通 p-adic étale 上同调群
DOI：
10.1023/a:1000556212097
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发表时间：
1999
影响因子：
1.8
通讯作者：
M. Ohta
中科院分区：
文献类型：
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作者：
M. Ohta
设素数p ≥ 5和与p互素的正整数N，考虑模曲线X1（Npr）和Y1（Npr）（r ≥ 1）的p-adic余上同调群的投影极限，分别记为ESp（N）Zp和GESp（N）Zp.设e* ′是投影到普通部分的ω i-本征空间的直和的投影，其中i ≠ 0，-1 mod p-1.我们的主要结果表明e* ′ GESp（N）Zp具有良好的p-adic Hodge结构，该结构可用λ-adic模形式描述，推广了e*′ ESp（N）Zp的已有结果.然后将Harder和Pink的方法应用于e*′ ESp（N）Zp上的Galois表示，构造了交换数域的分圆Zp -扩张上的大非分歧交换p-扩张.
Fix a prime number p ≥ 5 and a positive integer N prime to p. We consider the projective limits of p-adic étale cohomology groups of the modular curves X1(Npr) and Y1(Npr) (r ≥ 1), which are denoted by ESp(N) Zp and GES p(N)Zp , respectively. Let e* ′ be the projector to the direct sum of the ωi-eigenspaces of the ordinary part, for i ≢ 0, -1 mod p-1. Our main result states that e* ′ GESp (N)Zp has a good p-adic Hodge structure, which can be described in terms of λ-adic modular forms, extending the previously known result for e*′ ESp (N)Zp . We then apply the method of Harder and Pink to the Galois representation on e*′ ESp(N) Zp to construct large unramified abelian p-extensions over cyclotomic Zp -extensions of abelian number fields.