The basic locus of regular ramified unitary Rapoport-Zink spaces at vertex-stabilizer level

Abstract

We construct the Bruhat-Tits stratification of the reduced basic locus of regular ramified unitary Rapoport-Zink spaces of signature $(n\!-\!1,1)$ at vertex-stabilizer level. To study the Bruhat-Tits strata, we introduce strata models$\!-\!$simpler models that are \'{e}tale-locally isomorphic to each stratum. They admit two complementary characterizations: (i) as strict transforms under the blow-up of the local model at its worst point, and (ii) via a partial moduli description given by explicit linear-algebraic conditions; from these we deduce smoothness, explicit dimension formulas and irreducibility of the Bruhat-Tits strata.