论文标题
关于一些$ p $ -ADIC分析Hecke Actions的注释
A note on some $p$-adic analytic Hecke actions
论文作者
论文摘要
我们表明，Hecke运营商在（$ p $ ADIC）过度授权的模块化表单上的作用远离$ p $，在某种意义上是本地分析的（$ p $）。作为推论，Hecke代数的作用可以自然地扩展到刚性功能在其通用纤维上的作用。这直接决定了与过度会议特征形式相关的GALOIS表示的hodge-tate-sen权重，并确认了gouvêa的猜想。
We show that the action of Hecke operators away from $p$ on the space of ($p$-adic) overconvergent modular forms is ($p$-adically) locally analytic in a certain sense. As a corollary, the action of the Hecke algebra can be extended naturally to an action of rigid functions on its generic fiber. This directly determines the Hodge-Tate-Sen weights of Galois representation associated to an overconvergent eigenform and confirms a conjecture of Gouvêa.
