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arXiv · 2402.15107

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

Miaofen Chen·Jilong Tong
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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-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.

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Miaofen Chen, Jilong Tong. 2024-02-23. On the weak Harder-Narasimhan stratification on $B_{\mathrm{dR}}^+$-affine Grassmannian. https://arxiv.org/abs/2402.15107

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