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arXiv · 1805.07081

The Test Function Conjecture for Local Models of Weil-restricted groups

Thomas J. Haines·Timo Richarz
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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 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.

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Thomas J. Haines, Timo Richarz. 2018-05-18. The Test Function Conjecture for Local Models of Weil-restricted groups. https://doi.org/10.1112/s0010437x20007162

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