通过${\mathbb P}^1$的半稳定模型研究${\rm GL}(2,L)$的局部解析表示
表示论
2015-06-29 v3 数论
摘要
本文研究了有限扩张（的扩张）的整数环上射影直线的半稳定模型上的某些-adic 完备微分算子环层。这些层的全局截面可被识别为宽开同余子群的解析分布代数（及其中心约化）。研究表明，全局截面函子提供了相干模层范畴与分布代数上有限呈现模范畴之间的等价。利用 M. Emerton 的工作，我们随后在这些形式概形的射影极限上的层方面描述了的可容许表示。
引用
@article{arxiv.1410.1423,
title = {Locally analytic representations of ${\rm GL}(2,L)$ via semistable models of ${\mathbb P}^1$},
author = {Deepam Patel and Tobias Schmidt and Matthias Strauch},
journal= {arXiv preprint arXiv:1410.1423},
year = {2015}
}
备注
Added acknowledgement of support by the ANR program p-adic Hodge Theory and beyond (Th\'eHopaD). v3: section 6 now contains examples other than the first Drinfeld covering of the p-adic upper half plane, the new section 7 discusses in detail the admissibility of some representations furnished by the first Drinfeld covering of the p-adic upper half plane