论文标题
mod $ p $ galois表示的极端重量和驯服标准
Extremal weights and a tameness criterion for mod $p$ Galois representations
论文作者
论文摘要
我们研究了Serre猜想的重量部分，该猜想是通用$ n $ dimensional mod $ p $ galois表示。我们首先将Herzig的猜想推广到以$ p $为单位并证明我们猜想的重量方向的情况。然后，我们引入了与$ n $二维本地mod $ p $表示相关的新类别的权重，我们称为\ emph {xudrical stripter}。使用``Levi降低''特性的某些潜在结晶的galois变形空间，我们证明了这些权重的模块化。因此，我们推断了Serre在通用情况下某些分区代数的单位组的猜想的重量部分。
We study the weight part of Serre's conjecture for generic $n$-dimensional mod $p$ Galois representations. We first generalize Herzig's conjecture to the case where the field is ramified at $p$ and prove the weight elimination direction of our conjecture. We then introduce a new class of weights associated to $n$-dimensional local mod $p$ representations which we call \emph{extremal weights}. Using a ``Levi reduction" property of certain potentially crystalline Galois deformation spaces, we prove the modularity of these weights. As a consequence, we deduce the weight part of Serre's conjecture for unit groups of some division algebras in generic situations.
