Hodge 类与 Jacquet-Langlands 对应
数论
2023-07-12 v2
摘要
我们证明了四元数 Shimura 簇上上同调自守形式的 Jacquet-Langlands 对应由一个 Hodge 类实现。在 Kottwitz 关于酉相似群所附 Shimura 簇的猜想条件下，我们还证明了该 Hodge 类在 -进上同调中的像对所有 都是 Galois 不变的。
引用
@article{arxiv.1806.10563,
title = {Hodge classes and the Jacquet-Langlands correspondence},
author = {Atsushi Ichino and Kartik Prasanna},
journal= {arXiv preprint arXiv:1806.10563},
year = {2023}
}
备注
118 pages. Revised version following referee reports. Changes to introduction, Sec. 9 and Sec. 11, minor edits elsewhere. To be published in Forum of Math, Pi