论文标题
三维狂野分支的Galois表示的塞雷
Serre weights for three-dimensional wildly ramified Galois representations
论文作者
论文摘要
我们在通用条件下以$ p $毫无疑问的情况下在通用条件下为三维mod $ p $ galois表示的Serre猜想的重量部分。这删除了\ cite {arxiv：1512.06380}中的假设，\ cite {arxiv：1608.06570}，即表示表示为$ p $。我们还证明了Breuil的晶格猜想的一种版本和Mod $ p $多重性的结果$ u（3）$ - 算术歧管。关键输入是对Emerton的几何形状进行的研究 - 使用\ cite {arxiv：2007.05398}中引入的局部模型，使用局部模型。
We formulate and prove the weight part of Serre's conjecture for three-dimensional mod $p$ Galois representations under a genericity condition when the field is unramified at $p$. This removes the assumption in \cite{arXiv:1512.06380}, \cite{arXiv:1608.06570} that the representation be tamely ramified at $p$. We also prove a version of Breuil's lattice conjecture and a mod $p$ multiplicity one result for the cohomology of $U(3)$-arithmetic manifolds. The key input is a study of the geometry of the Emerton--Gee stacks \cite{arXiv:2012.12719} using the local models introduced in \cite{arXiv:2007.05398}.
