Bruhat-Tits stratification for the GU(1,n-1) Shimura variety with parahoric reduction over an inert prime

Abstract: The basic locus of certain Shimura varieties is known to be stratified by (classical) Deligne-Lusztig varieties. Such a stratification is usually called the Bruhat-Tits stratification, because the incidence relation is expected to be determined by the Bruhat-Tits building of some related p-adic group. By the work of Görtz-He-Nie on affine Deligne-Lusztig varieties, we know precisely which Shimura varieties must admit a Bruhat-Tits stratification. However, determining the actual incidence relations usually requires a case-by-case analysis. In this talk, we consider PEL unitary Shimura varieties of signature (1,n-1) over an inert prime. For these varieties, so far the Bruhat-Tits stratification had only been described for hyperspecial level (Vollaard-Wedhorn) and maximal parahoric level (Cho). Building upon these works, we describe the stratification for arbitrary parahoric levels. If time permits, we will discuss how the Bruhat-Tits stratification compares with the EKOR strata on the basic locus.

number theory

Audience: researchers in the topic

Postech-PMI Number Theory Seminar