抛物特征簇的过收敛上同调
Parabolic eigenvarieties via overconvergent cohomology
摘要：
设$G'$是$\mathbb{Q}$上的连通约化群，使得$G = G'/\mathbb{Q}_p$是拟分裂的，$Q \subset G$是抛物子群.引入了关于$Q$的仿射过收敛上同调群，并证明了一个经典性定理，证明了这类群的小斜率部分与经典上同调的小斜率部分一致.这允许使用超收敛上同调parahoric，而不是Iwahoric，水平，并提供了灵活的提升定理，似乎是特别适合算术应用。当$Q$是Borel时，我们恢复了通常的过收敛上同调理论，并且我们的经典性定理给出了比现有文献更强的斜率界.我们用我们的理论来构造$Q$ -抛物型本征簇，它参数化$p$ -adic族的Hecke本征值系统，在$Q$是有限的斜率，但允许无限的斜率远离$Q$。
英文摘要：
Let $G'$ be a connected reductive group over $\mathbb{Q}$ such that $G = G'/\mathbb{Q}_p$ is quasi-split, and let $Q \subset G$ be a parabolic subgroup. We introduce parahoric overconvergent cohomology groups with respect to $Q$, and prove a classicality theorem showing that the small slope parts of these groups coincide with those of classical cohomology. This allows the use of overconvergent cohomology at parahoric, rather than Iwahoric, level, and provides flexible lifting theorems that appear to be particularly well-adapted to arithmetic applications. When $Q$ is the Borel, we recover the usual theory of overconvergent cohomology, and our classicality theorem gives a stronger slope bound than in the existing literature. We use our theory to construct $Q$-parabolic eigenvarieties, which parametrise $p$-adic families of systems of Hecke eigenvalues that are finite slope at $Q$, but that allow infinite slope away from $Q$.
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