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  1. (, International Mathematics Research Notices)
    Abstract We develop a Tannakian framework for group-theoretic analogs of displays, originally introduced by Bültel and Pappas, and further studied by Lau. We use this framework to define Rapoport–Zink functors associated to triples $$(G,\{\mu \},[b])$$, where $$G$$ is a flat affine group scheme over $${\mathbb{Z}}_p$$ and $$\mu$$ is a cocharacter of $$G$$ defined over a finite unramified extension of $${\mathbb{Z}}_p$$. We prove these functors give a quotient stack presented by Witt vector loop groups, thereby showing our definition generalizes the group-theoretic definition of Rapoport–Zink spaces given by Bültel and Pappas. As an application, we prove a special case of a conjecture of Bültel and Pappas by showing their definition coincides with that of Rapoport and Zink in the case of unramified EL-type local Shimura data. 
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  2. (, Journal of Algebra)
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  3. ; (, Journal of the American Mathematical Society)
    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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  4. ; (, Duke Mathematical Journal)
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  5. ; (, Compositio Mathematica)
    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 $$p\geqslant 5$$ . 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. 
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