Overconvergent Eichler–Shimura isomorphisms
Overconvergent Eichler–Shimura isomorphisms
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过收敛的艾希勒-志村同构
DOI：
10.1017/s1474748013000364
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发表时间：
2013
影响因子：
0.9
通讯作者：
G. Stevens
中科院分区：
文献类型：
--
作者：
F. Andreatta;A. Iovita;G. Stevens
给定素数p\gt 2，整数h\geq 0，在权空间W中的大开圆盘U，我们从U上过收敛模符号的解析族空间中构造了一个Hecke-Galois等变态射U，到对应的超收敛模形式的解析族空间，都具有${ \mathbb{C} }_{p} $ -系数。我们表明，有一个有限的子集$Z$的$U$，这个态射诱导一个$p$ -adic分析家庭的同构有关的超收敛模符号的重量$k$和斜率$\leq h$的超收敛模形式的重量$k+ 2$和斜率$\leq h$。
Abstract Given a prime $p\gt 2$ , an integer $h\geq 0$ , and a wide open disk $U$ in the weight space $ \mathcal{W} $ of ${\mathbf{GL} }_{2} $ , we construct a Hecke–Galois-equivariant morphism ${ \Psi }_{U}^{(h)} $ from the space of analytic families of overconvergent modular symbols over $U$ with bounded slope $\leq h$ , to the corresponding space of analytic families of overconvergent modular forms, all with ${ \mathbb{C} }_{p} $ -coefficients. We show that there is a finite subset $Z$ of $U$ for which this morphism induces a $p$ -adic analytic family of isomorphisms relating overconvergent modular symbols of weight $k$ and slope $\leq h$ to overconvergent modular forms of weight $k+ 2$ and slope $\leq h$ .