TITLE: Non emptyness of ordinary locus for PEL type Shimura varieties
QUESTION [8 upvotes]: We let $B$ be a simple algebra over $\mathbb Q$, with the usual notations for PEL type Shimura varieties. In his paper "Ordinariness in good reductions of Shimura varieties of PEL-type" (available here http://archive.numdam.org/article/ASENS_1999_4_32_5_575_0.pdf), Wedhorn proved, under the assumption that $p$ is unramified in $B$, that the ordinary locus in (the reduction) a PEL type Shimura variety is non-empty if and only if it is dense if and only if $p$ splits completely in the reflex field.
So my question is the following:
Are there similar results, even partial, without the unramifiedness assumption?

REPLY [3 votes]: In the case of Iwahori level structure, there is the result of Stamm (cited in Wedhorn's paper) who gives an example where the ordinary locaus fails to be dense (Hilbert-Blumenthal case).
Stamm's result is reproved and generalized in
Philipp Hartwig, Kottwitz-Rapoport and p-rank strata in the reduction of Shimura varieties of PEL type,
who shows that, still in the Iwahori case (loc.cit. Theorem 1.1.1):
Assume that $\mathcal B$ is the symplectic PEL datum associated with a totally real extension $F/\mathbb Q$. Assume that there is only a single prime of $\mathcal O_F$ dividing $p$. Then the ordinary locus lies dense in $\mathcal A_F$ if and only if $p$ is totally ramified in $\mathcal O_F$.
Of course, if the ordinary locaus is dense in the Iwahori case, then the same is true for all parahoric level structures.