The basic locus of ramified unitary Shimura varieties of signature $(n-1,1)$ at maximal vertex level

Abstract

We construct the Bruhat--Tits stratification of the reduced locus of the ramified unitary Rapoport--Zink space of signature $(n-1,1)$, with the level being the stabilizer of a vertex lattice. We develop the local model theory for Bruhat--Tits strata, proving their normality and Cohen--Macaulayness, and provide precise dimension formulas. Additionally, we establish an explicit scheme-theoretical isomorphism between Bruhat--Tits strata and Deligne--Lusztig varieties.

Major revision: improved the writing and clarified parts of the content; fixed several gaps and mistakes; added an appendix on display theory