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Award ID contains: 2200873

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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. (, Épijournal de Géométrie Algébrique)
    This article proves, in the case of split groups over arbitrary fields, that all fibers of convolution morphisms attached to parahoric affine flag varieties are paved by products of affine lines and affine lines minus a point. This applies in particular to the affine Grassmannian and to the convolution morphisms in the context of the geometric Satake correspondence. The second part of the article extends these results over $$\mathbb Z$$. Those in turn relate to the recent work of Cass-van den Hove-Scholbach on the geometric Satake equivalence for integral motives, and provide some alternative proofs for some of their results. Comment: 24 pages. Minor error corrected with the addition of Lemma 7.2. Lemma 7.3 added. Material on triviality of morphisms added to section 5. Minor changes in notation. Published version 
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    Free, publicly-accessible full text available May 16, 2026
  3. ; ; (, Annales Scientifiques de l'École Normale Supérieure)
    Full Text Available 
  4. (, Journal of the Ramanujan Mathematical Society)
    Accepted Manuscript Full Text Available