论文标题
模块化形式的塞雷重量和Breuil-Mézard的猜想
Serre weights and the Breuil-Mézard conjecture for modular forms
论文作者
论文摘要
Serre的强烈猜想，如今是Khare和Wintenberger的定理，指出，每二维连续，奇怪，不可减少的mod $ p $ p $ galois代表$ρ$来自特定最小重量$ k（ρ）$的模块化形式，级别$ n（ρ）$ n（ρ）$ n（ρ）$ n（ρ）$（ρ）$ $（ρ）。在这篇简短的论文中，我们表明，最小的重量$ k（ρ）$等于受Buzzard，Diamond和Jarvis引入的重量配方启发的最小重量概念。此外，使用Breuil-Mézard的猜想，我们表明，这两个权重配方均等于最小的$ k \ geq 2 $，因此$ρ$具有霍奇 - 泰特型型$（0，k-1）$的结晶升降。
Serre's strong conjecture, now a theorem of Khare and Wintenberger, states that every two-dimensional continuous, odd, irreducible mod $p$ Galois representation $ρ$ arises from a modular form of a specific minimal weight $k(ρ)$, level $N(ρ)$ and character $ε(ρ)$. In this short paper we show that the minimal weight $k(ρ)$ is equal to a notion of minimal weight inspired by the recipe for weights introduced by Buzzard, Diamond and Jarvis. Moreover, using the Breuil-Mézard conjecture we show that both weight recipes are equal to the smallest $k \geq 2$ such that $ρ$ has a crystalline lift of Hodge-Tate type $(0,k-1)$.
