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Creators/Authors contains: "Richarz, Timo"

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  1. ; ; ; (, Mathematische Annalen)
    Abstract We construct local models of Shimura varieties and investigate their singularities, with special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary groups in residue characteristic 2 we construct local models, show reducedness of their special fiber, Cohen–Macaulayness and in equicharacteristic also (pseudo-)rationality. In mixed characteristic we conjecture their pseudo-rationality. This is based on the construction of parahoric group schemes over two dimensional bases for wildly ramified groups and an analysis of singularities of the attached Schubert varieties in positive characteristic using perfect geometry. 
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    Free, publicly-accessible full text available April 1, 2026
  2. ; ; (, Annales Scientifiques de l'École Normale Supérieure)
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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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