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

Kieu Hieu Nguyen; Eva Viehmann

doi:10.1112/S0010437X23007066

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

Kieu Hieu Nguyen, Eva Viehmann

University of Münster

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Pages (from-to)	711-745
Number of pages	35
Journal	Compositio Mathematica
Volume	159
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X23007066
State	Published - 29 Apr 2023
Externally published	Yes

Keywords

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

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10.1112/S0010437X23007066

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AB - 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.

KW - B-Grassmannian

KW - Harder-Narasimhan stratification

KW - p-adic period domain

KW - weakly admissible locus

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JO - Compositio Mathematica

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ER -

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

Abstract

Keywords

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