Generic vanishing theory in positive characteristic

Jefferson Baudin

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arXiv · 2507.00771

Generic vanishing theory in positive characteristic

Jefferson Baudin

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Abstract

We simplify and improve the main fundamental theorems of positive characteristic generic vanishing theory. As a quick corollary of the theory, we prove that a normal variety $X$ of maximal Albanese dimension satisfies $H^0(X, \omega_X) \neq 0$ and that if $\mathrm{Alb}(X)$ is ordinary, then $S^0(X, \omega_X) \neq 0$.

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Jefferson Baudin. 2025-07-01. Generic vanishing theory in positive characteristic. https://arxiv.org/abs/2507.00771

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