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Hauptverfasser: Chen, Miaofen, Tong, Jilong
Format: Preprint
Veröffentlicht: 2024
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Online-Zugang:https://arxiv.org/abs/2402.15107
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author Chen, Miaofen
Tong, Jilong
author_facet Chen, Miaofen
Tong, Jilong
contents We consider the Harder-Narasimhan formalism on the category of normed isocrystals and show that the Harder-Narasimhan filtration is compatible with tensor products which generalizes a result of Cornut. As an application of this result, we are able to define a (weak) Harder-Narasimhan stratification on the $B_{\mathrm{dR}}^+$-affine Grassmannian for arbitrary $(G, b, μ)$. When $μ$ is minuscule, it corresponds to the Harder-Narasimhan stratification on the flag varieties defined by Dat-Orlik-Rapoport. And when $b$ is basic, it's studied by Nguyen-Viehmann and Shen. We study the basic geometric properties of the Harder-Narasimhan stratification, such as non-emptiness, dimension and its relation with other stratifications.
format Preprint
id arxiv_https___arxiv_org_abs_2402_15107
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the weak Harder-Narasimhan stratification on $B_{\mathrm{dR}}^+$-affine Grassmannian
Chen, Miaofen
Tong, Jilong
Algebraic Geometry
We consider the Harder-Narasimhan formalism on the category of normed isocrystals and show that the Harder-Narasimhan filtration is compatible with tensor products which generalizes a result of Cornut. As an application of this result, we are able to define a (weak) Harder-Narasimhan stratification on the $B_{\mathrm{dR}}^+$-affine Grassmannian for arbitrary $(G, b, μ)$. When $μ$ is minuscule, it corresponds to the Harder-Narasimhan stratification on the flag varieties defined by Dat-Orlik-Rapoport. And when $b$ is basic, it's studied by Nguyen-Viehmann and Shen. We study the basic geometric properties of the Harder-Narasimhan stratification, such as non-emptiness, dimension and its relation with other stratifications.
title On the weak Harder-Narasimhan stratification on $B_{\mathrm{dR}}^+$-affine Grassmannian
topic Algebraic Geometry
url https://arxiv.org/abs/2402.15107