We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure attached to Weil-restricted groups, as defined by B. Levin. Our result covers the (modified) local models attached to all connected reductive groups over $p$-adic local fields with $p\geq 5$. In addition, we give a self-contained study of relative affine Grassmannians and loop groups formed using general relative effective Cartier divisors in a relative curve over an arbitrary Noetherian affine scheme.

中文翻译：

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Weil限制群局部模型的检验函数猜想

我们证明了 Kottwitz 和第一作者的测试函数猜想，用于 Shimura 品种的本地模型，其具有依附于 Weil 限制群的平行水平结构，如 B. Levin 所定义。我们的结果涵盖了在 $p\geq 5$ 的 $p$-adic 局部域上附加到所有连接的还原组的（修改的）局部模型。此外，我们对在任意诺特仿射方案上的相对曲线中使用一般相对有效卡地亚除数形成的相对仿射格拉斯曼和环群进行了独立研究。