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arXiv · 2507.13452

Generic vanishing on homogeneous spaces in arbitrary characteristic

Ankit Rai·K. V. Shuddhodan
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Abstract

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 \[ (-1)^{\dim X-\dim W+\dim Z}\chi(gW\cap Z)\geq 0 \] for generic $g\in G$. This extends the characteristic-zero theorem of Sch\"urmann--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.

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Ankit Rai, K. V. Shuddhodan. 2025-07-17. Generic vanishing on homogeneous spaces in arbitrary characteristic. https://arxiv.org/abs/2507.13452

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