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arXiv · 2202.06691

Vanishing results for the coherent cohomology of automorphic vector bundles over the Siegel variety in positive characteristic

Thibault Alexandre
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Abstract

We prove vanishing results for the coherent cohomology of the good reduction modulo $p$ of the Siegel variety with coefficients in some automorphic bundles. We show that for an automorphic bundle with highest weight $\lambda$ near the walls of the anti-dominant Weyl chamber, there is an integer $e \geq 0$ such that the cohomology is concentrated in degrees $[0, e]$. The accessible weights with our method are not necessarily regular and not necessarily $p$-small. Since our method is technical, we also provide an algorithm written in Sage that computes explicitly the vanishing results.

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Thibault Alexandre. 2022-02-14. Vanishing results for the coherent cohomology of automorphic vector bundles over the Siegel variety in positive characteristic. https://doi.org/10.2140/ant.2025.19.143

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