论文标题
局部gouvêa-mazur猜想
Localized Gouvêa-Mazur conjecture
论文作者
论文摘要
当重量变化$ p $时，Gouvêa-Mazur [GM]对模块化形式的斜率斜率的局部构成做出了猜想。由于可以根据相关的残留Galois表示将模块化形式的空间分解，因此Gouvêa-Mazur的猜想对于每个这样的组件都是有意义的。当残留的galois表示不可约时，并且限制$ \ textrm {gal}（\ overline {\ mathbb {q}} _ p/p/\ mathbb {q} _p）$是可还原和非常普通的。
Gouvêa-Mazur [GM] made a conjecture on the local constancy of slopes of modular forms when the weight varies $p$-adically. Since one may decompose the space of modular forms according to associated residual Galois representations, the Gouvêa-Mazur conjecture makes sense for each such component. We prove the localized Gouvêa-Mazur conjecture when the residual Galois representation is irreducible and its restriction to $\textrm{Gal}(\overline{\mathbb{Q}}_p/\mathbb{Q}_p)$ is reducible and very generic.
