Grassmanniennes affines tordues sur les entiers

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.

Automated summary

This paper generalizes the previous works on twisted affine Grassmannians to the wildly ramified case, with mild assumptions. It constructs 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, and their $\mathbb {F}_p [\hspace{-0.5mm}[ {t} ]\hspace {-0.5mm}]$-models are parahoric in a generalized sense. The paper also studies their affine Grassmannians and proves the normality of Schubert varieties and Zhu's coherence theorem.