ON NEWTON STRATA IN THE BdRC -GRASSMANNIAN

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Abstract

We study parabolic reductions and Newton points of G-bundles on the Fargues–Fontaine curve and the Newton stratification on the BdRC -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 jBunGj 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 BdRC -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.

Original languageEnglish
Pages (from-to)177-225
Number of pages49
JournalDuke Mathematical Journal
Volume173
Issue number1
DOIs
StatePublished - 2024
Externally publishedYes

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