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

TL;DR

This paper constructs and analyzes the Bruhat-Tits stratification of the basic locus in ramified unitary Rapoport-Zink spaces, providing explicit models, smoothness, and dimension formulas for the strata.

Contribution

It introduces simpler strata models for the basic locus, characterizes them via blow-ups and linear algebra, and proves their smoothness and irreducibility.

Findings

Explicit dimension formulas for Bruhat-Tits strata

Smoothness and irreducibility of the strata

Models characterized by blow-ups and linear conditions

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.