Bruhat strata for Shimura varieties of PEL type
arXiv:1303.0115 · doi:10.1007/s00209-013-1274-2
Abstract
The Bruhat stratification for Shimura varieties of PEL type is studied. In the Siegel case this stratification is a scheme-theoretic variant of the stratification by the a-number. We show that all Bruhat strata are smooth and determine their dimensions. We also prove that the closure of a Bruhat stratum is a union of Bruhat strata and describe which Bruhat strata are contained in the closure of a given Bruhat stratum.
18 pages, minor additions, main results unchanged, to appear in Math. Zeitschrift