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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.15107 |
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| _version_ | 1866916135642857472 |
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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 |