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On the weak Harder–Narasimhan stratification on $B_{\mathrm{dR}}^+$-affine Grassmannian

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  15 December 2025

Miaofen Chen  and
Jilong Tong
Miaofen Chen
Affiliation:
Shanghai Center for Mathematical Sciences, Fudan University, 2005 Songhu Road, Shanghai 20438, China miaofenchen@fudan.edu.cn
Jilong Tong
Affiliation:
School of Mathematical Sciences, Capital Normal University, 105, Xi San Huan Bei Lu, Beijing 100048, China jilong.tong@cnu.edu.cn
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Abstract

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 $(G, b, \mu)$. When $\mu$ is minuscule, it corresponds to the Harder–Narasimhan stratification on the flag varieties defined by Dat, Orlik and Rapoport. Moreover, when b is basic, it has been studied by Nguyen and 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.

Keywords

p-adic period domainsHarder–Narasimhan stratificationweakly admissible locus

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 14G20: Local ground fields

Information

Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 10 , October 2025 , pp. 2654 - 2711
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

In memory of Professor Linsheng Yin

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