Smoothness of Schubert varieties in twisted affine Grassmannians
Thomas J. Haines, Timo Richarz
TL;DR
This paper classifies smooth and rationally smooth Schubert varieties in twisted affine Grassmannians for tamely ramified groups, with implications for Shimura varieties and their reduction properties.
Contribution
It provides a complete list of smooth and rationally smooth Schubert varieties in twisted affine Grassmannians, including the quasi-minuscule case for ramified triality.
Findings
Complete classification of smooth Schubert varieties
Identification of rationally smooth cases
Application to Shimura varieties with good reduction
Abstract
We give a complete list of smooth and rationally smooth normalized Schubert varieties in the twisted affine Grassmannian associated with a tamely ramified group and a special vertex of its Bruhat-Tits building. The particular case of the quasi-minuscule Schubert variety in the quasi-split but non-split form of ("ramified triality") provides an input needed in the article by He-Pappas-Rapoport classifying Shimura varieties with good or semi-stable reduction.
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