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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2507.13452 |
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| _version_ | 1866909054416191488 |
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| author | Rai, Ankit Shuddhodan, K. V. |
| author_facet | Rai, Ankit Shuddhodan, K. V. |
| contents | Let $X$ be a proper homogeneous space for a connected algebraic group $G$ over an algebraically closed field. For locally closed smooth affine subvarieties $W,Z\subset X$, we show that \[ (-1)^{\dim X-\dim W+\dim Z}χ(gW\cap Z)\geq 0 \] for generic $g\in G$. This extends the characteristic-zero theorem of Schürmann--Simpson--Wang. Over finite fields, our methods give a trace-function identity on a dense open subset of $G$ and a Lang--Weil estimate for the non-generic locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic vanishing on homogeneous spaces in arbitrary characteristic Rai, Ankit Shuddhodan, K. V. Algebraic Geometry Let $X$ be a proper homogeneous space for a connected algebraic group $G$ over an algebraically closed field. For locally closed smooth affine subvarieties $W,Z\subset X$, we show that \[ (-1)^{\dim X-\dim W+\dim Z}χ(gW\cap Z)\geq 0 \] for generic $g\in G$. This extends the characteristic-zero theorem of Schürmann--Simpson--Wang. Over finite fields, our methods give a trace-function identity on a dense open subset of $G$ and a Lang--Weil estimate for the non-generic locus. |
| title | Generic vanishing on homogeneous spaces in arbitrary characteristic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.13452 |