Geodesic
Grassmanniennes affines tordues sur les entiers
Forum of Mathematics, Sigma, Tome 11 (2023)

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We generalize the works of Pappas–Rapoport–Zhu on twisted affine Grassmannians to the wildly ramified case under mild assumptions. This rests on a construction of certain smooth affine $\mathbb {Z}[t]$-groups with connected fibers of parahoric type, motivated by previous work of Tits. The resulting $\mathbb {F}_p(t)$-groups are pseudo-reductive and sometimes non-standard in the sense of Conrad–Gabber–Prasad, and their $\mathbb {F}_p [\hspace {-0,5mm}[ {t} ]\hspace {-0,5mm}] $-models are parahoric in a generalized sense. We study their affine Grassmannians, proving normality of Schubert varieties and Zhu’s coherence theorem. 
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     author = {Jo\~ao Louren\c{c}o},
     title = {Grassmanniennes affines tordues sur les entiers},
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João Lourenço. Grassmanniennes affines tordues sur les entiers. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.4

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