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

Abstract

We study the Newton stratification in the B + dR -Grassmannian for GLn associated to an arbitrary (possibly nonbasic) element of B(GLn). Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in B(GLn), 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.Contents 14 3.3. An explicit classification of nonempty Newton strata 15 References 20