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

Abstract

We study the Newton stratification in the B_{\mathrm{dR}}^{+} -Grassmannian for \mathrm{GL}_{n} associated to an arbitrary (possibly nonbasic) element of B(\mathrm{GL}_{n}) . Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in B(\mathrm{GL}_{n}) , our classification is given by some explicit conditions in terms of Newton polygons. For the proof, we proceed by induction on n using a previous result of the author that classifies all extensions of two given vector bundles on the Fargues–Fontaine curve.