论文标题
二维GALOIS表示的显式Serre重量在分支的基础上
Explicit Serre weights for two-dimensional Galois representations over a ramified base
论文作者
论文摘要
给定一个完全真实的数字字段$ f $和a mod $ p $ galois表示$ρ\ colon g_f \ to \ mathrm {gl} _2（\ bar {\ bar {\ mathbf {f}} _ p）$，我们建议对Serre Wights $ w（ρ）$ nctacte to $ρ$ $ρ$ pect to $ρ$。我们证明我们的明确定义等于文献中可用的定义。结果，我们在完全真实的数字字段上获得了希尔伯特模块化形式的显式Serre模块化猜想。我们的工作概括了Dembélé的先前工作 - 迪蒙德 - 罗伯茨和卡莱加里 - 埃默顿 - 盖伊 - 马车 - 当$ f $中毫无疑问时，它们共同给出了显式和同等的重量。
Given a totally real number field $F$ and a mod $p$ Galois representation $ρ\colon G_F\to \mathrm{GL}_2(\bar{\mathbf{F}}_p)$, we propose an explicit definition of the set of Serre weights $W(ρ)$ attached to $ρ$. We prove that our explicit definition is equivalent to previous definitions available in the literature. As a consequence we obtain an explicit Serre's modularity conjecture for Hilbert modular forms over totally real number fields. Our work generalises previous work of Dembélé--Diamond--Roberts and Calegari--Emerton--Gee--Mavrides which together give explicit and equivalent sets of weights when $p$ is unramified in $F$.
