Hodge classes and the Jacquet–Langlands correspondence
Hodge classes and the Jacquet–Langlands correspondence
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DOI：
10.1017/fmp.2023.20
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发表时间：
2018-06
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影响因子：
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通讯作者：
Atsushi Ichino;Kartik Prasanna
中科院分区：
文献类型：
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作者：
Atsushi Ichino;Kartik Prasanna
本文证明了四元数Shimura簇上同调自守型的Jacquet-Langlands对应是由一个Hodge类实现的。条件Kottwitz的猜想志村品种重视酉相似群，我们还表明，图像的霍奇类在$\ell $ -adic上同调是伽罗瓦不变的所有$\ell $。
Abstract We prove that the Jacquet–Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz’s conjecture for Shimura varieties attached to unitary similitude groups, we also show that the image of this Hodge class in $\ell $ -adic cohomology is Galois invariant for all $\ell $ .