A Harder-Narasimhan stratification of the B+dR-Grassmannian

Kieu Hieu Nguyen, Eva Viehmann

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2 Scopus citations

Abstract

We establish a Harder-Narasimhan formalism for modifications of -bundles on the Fargues-Fontaine curve. The semi-stable stratum of the associated stratification of the B+dR-Grassmannian coincides with the variant of the weakly admissible locus defined by Viehmann, and its classical points agree with those of the basic Newton stratum. When restricted to minuscule affine Schubert cells, the stratification corresponds to the Harder-Narasimhan stratification of Dat, Orlik and Rapoport. We also study basic geometric properties of the strata, and the relation to the Hodge-Newton decomposition.

Original languageEnglish
Pages (from-to)711-745
Number of pages35
JournalCompositio Mathematica
Volume159
Issue number4
DOIs
StatePublished - 29 Apr 2023
Externally publishedYes

Keywords

  • B-Grassmannian
  • Harder-Narasimhan stratification
  • p-adic period domain
  • weakly admissible locus

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