论文标题
Fargues的兼容性 - 单一组的近chol对应
Compatibility of the Fargues--Scholze correspondence for unitary groups
论文作者
论文摘要
我们研究了奇数变量中未受到的统一和统一相似组。利用第一个和第三名的作者在Kottwitz猜想中为象征组的作品的作品，我们表明，Fargues-Scholze Local Langlands对应关系与MOK构建的本地Langlands对应关系的半简化，我们考虑的组是MOK构建的。然后将此兼容性结果与fargues-scholze构建的光谱作用结合在一起，以验证其对超级质量$ \ ell $ parameters的本地Langlands猜想的分类形式。我们推断出Fargues的Eigensheaf猜想，并证明了Kottwitz对我们考虑的组的最强形式，即使在非微小$μ$的情况下也是如此。
We study unramified unitary and unitary similitude groups in an odd number of variables. Using work of the first and third named authors on the Kottwitz Conjecture for the similitude groups, we show that the Fargues--Scholze local Langlands correspondence agrees with the semi-simplification of the local Langlands correspondences constructed by Mok for the groups we consider. This compatibility result is then combined with the spectral action constructed by Fargues--Scholze, to verify their categorical form of the local Langlands conjecture for supercuspidal $\ell$-parameters. We deduce Fargues' eigensheaf conjecture and prove the strongest form of Kottwitz's conjecture for the groups we consider, even in the case of non minuscule $μ$.
