On nonemptiness of Newton strata in the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GSp}_{2n}$

TL;DR

This paper classifies which Newton strata are nonempty in the $B_{dR}^+$-Grassmannian for $ ext{GSp}_{2n}$, providing explicit criteria based on Frobenius-conjugacy classes and Newton polygons.

Contribution

It offers an explicit classification of nonempty Newton strata in the $B_{dR}^+$-Grassmannian for $ ext{GSp}_{2n}$, extending previous work with new criteria.

Findings

Explicit classification of nonempty Newton strata

Criteria based on Frobenius-conjugacy classes

Conditions on Newton polygons

Abstract

We build upon our previous work to study the Newton stratification on the $B_\mathrm{dR}^+$-Grassmannian for $\mathrm{GSp}_{2n}$. Our main result gives an explicit classification of all nonempty Newton strata associated to a Frobenius-conjugacy class satisfying certain conditions on the Newton polygon.