On nonemptiness of Newton strata in the B_dR⁺-Grassmannian for GL_n

2022/09/17 by Serin Hong, Hong, Serin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2209.08374

Abstract

We study the Newton stratification in the B_dR⁺-Grassmannian for GL_n associated to an arbitrary (possibly nonbasic) element of B(GL_n). Our main result classifies all nonempty Newton strata in an arbitrary minuscule Schubert cell. For a large class of elements in B(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.

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