Stratification des vari\'et\'es de Hilbert en pr\'esence de ramification

Abstract

In this paper we study the geometry of the special fiber of Pappas-Rapoport models of Shimura varieties in the Hilbert case. More precisely we prove that the stratification induced by the Hodge polygon is a good stratification, which is false in the Hilbert-Siegel case for $g\geq 2$. Then we use known results on the convolution product of affine Grassmannians to describe the dimension of the strata and obtain that the forgetting morphism to the Kottwitz PEL model is flat in restriction to Hodge strata.