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On Newton strata in the BdR+-Grassmannian

Eva Viehmann

2024Duke Mathematical Journal11 citationsDOI

Abstract

We study parabolic reductions and Newton points of G-bundles on the Fargues–Fontaine curve and the Newton stratification on the BdR+-Grassmannian for any reductive group G. Let BunG be the stack of G-bundles on the Fargues–Fontaine curve. Our first main result is to show that under the identification of the points of BunG with Kottwitz’s set B(G), the closure relations on |BunG| coincide with the opposite of the usual partial order on B(G). Furthermore, we prove that every non-Hodge–Newton decomposable Newton stratum in a minuscule affine Schubert cell in the BdR+-Grassmannian intersects the weakly admissible locus, proving a conjecture of Chen. On the way, we study several interesting properties of parabolic reductions of G-bundles, and we determine which Newton strata have classical points.

Topics & Concepts

GrassmannianMathematicsLocus (genetics)ConjecturePure mathematicsStratification (seeds)Affine transformationReductive groupSchubert calculusCombinatoricsMathematical analysisBotanyGroup theoryBiologyGerminationSeed dormancyBiochemistryChemistryGeneDormancyAdvanced Algebra and GeometryAlgebraic Geometry and Number TheoryGeometry and complex manifolds
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