The test function conjecture for local models of Weil-restricted groups

Abstract

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 toallconnected reductive groups over$p$-adic local fields with$p\geqslant 5$. 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.