论文标题
抛物线特征性通过过度会议的共同学
Parabolic eigenvarieties via overconvergent cohomology
论文作者
论文摘要
令$ g'$为$ \ mathbb {q} $上的连接还原组，这样$ g = g = g = g'/\ mathbb {q} _p $是quasi-split，然后让$ q \ subset g $为抛物线子组。我们介绍了关于$ Q $的帕亚里克过度会议的共同体学组，并证明了经典定理，表明这些组的小斜率部分与经典共同体学的部分相吻合。这允许使用过度融合的共同体学，而不是伊瓦里奇（Iwahoric），并提供了柔性的提升定理，这些定理似乎特别适应算术应用。当$ q $是Borel时，我们恢复了通常的过度会议的同谋理论，而我们的经典定理给出了比现有文献更强的斜率界限。我们使用理论来构建$ Q $ - 寄生虫特征瓦里埃蒂（$ p $ p $ p $ a的hecke eigenvalues系统），它们是$ q $ $ q $的有限斜率，但这允许无限斜率远离$ q $。
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 $Q$.
