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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13452 |
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Table of 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.