Dualizing complexes on the moduli of parabolic bundles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915420687040512 |
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| author | Hamann, Linus Imai, Naoki |
| author_facet | Hamann, Linus Imai, Naoki |
| contents | For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on $\mathrm{Bun}_P$, the moduli stack of $P$-bundles on the Fargues--Fontaine curve, can be described explicitly in terms of the modulus character of $P$. As applications, we identify various characters appearing in the theory of local and global Shimura varieties, show the Harris--Viehmann conjecture in the Hodge--Newton reducible case, and carry out some computations of the geometric Eisenstein functors for general parabolics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06342 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dualizing complexes on the moduli of parabolic bundles Hamann, Linus Imai, Naoki Number Theory Algebraic Geometry Representation Theory For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on $\mathrm{Bun}_P$, the moduli stack of $P$-bundles on the Fargues--Fontaine curve, can be described explicitly in terms of the modulus character of $P$. As applications, we identify various characters appearing in the theory of local and global Shimura varieties, show the Harris--Viehmann conjecture in the Hodge--Newton reducible case, and carry out some computations of the geometric Eisenstein functors for general parabolics. |
| title | Dualizing complexes on the moduli of parabolic bundles |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2401.06342 |