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

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 Added by Timo Richarz
 Publication date 2018
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and research's language is English




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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 $pgeq 5$. 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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We prove the test function conjecture of Kottwitz and the first named author for local models of Shimura varieties with parahoric level structure, and their analogues in equal characteristic.
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