# Newton point and Newton polygon stratifications

Let $k$ be a field of characteristic $p>0$, with absolute Galois group $\Gamma$. Let $Y$ be a Shimura variety of PEL type, defined over $k$, with associated reductive (connected) quasisplit group $G$. We fix a maximal torus $T$ of $G_{\overline k}$ and a Borel subgroup $B \supset T$. We get a root datum $(X^\ast,R^\ast,X_\ast,R_\ast, \Delta)$, and let $\Omega$ be the Weyl group.

We have the so called Newton stratification of $Y$, that is defined in terms of the Newton point of any $y \in Y$. This is defined taking the F-isocrystal associated to $y$ and considering its image in $$(X_{\ast,\mathbb Q}/\Omega)^\Gamma$$ via the "Newton map". See "On the classification and specialization of F-isocrystals with additional structure", by Rapoport and Richartz.

On the other hand, we can consider the stratification given by the Newton polygon of the F-isocrystal (i.e. looking at the classical Newton polygon of the abelian variety given by $y$). This stratification can be obtained as above forgetting the $G$-structure via the natural morphism $G \to \operatorname{GL}(V)$ (where $V$ is part of the PEL datum). In particular, the Newton point stratification is finer than the Newton polygon stratification.

Question: are these two stratifications equal?

This is the case if $G=\operatorname{GL}$ or $G$ is the symplectic group (I think), so, using the standard terminology of PEL Shimura variety, in case (A)linear or in case (C). It remains the unitary case, where I think the answer is in genera "no". Can someone give an example?

Thank you very much!

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