Generic vanishing theory in positive characteristic

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 proper variety X of maximal Albanese dimension satisfies H^{0}(X, \omega_{X}) \neq 0 . If \operatorname{Alb}(X) is in addition ordinary, then S^{0}(X, \omega_{X}) \neq 0 .

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Publication Details

Journal
L’Enseignement Mathématique
Published
2026-07-16
DOI
https://doi.org/10.4171/lem/1106
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
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article

Generic vanishing theory in positive characteristic

Jefferson Baudin
L’Enseignement Mathématique
Algebraic Geometry and Number Theory
article

Generic vanishing theory in positive characteristic

Jefferson Baudin
article en

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 proper variety X of maximal Albanese dimension satisfies H^{0}(X, \omega_{X}) \neq 0 . If \operatorname{Alb}(X) is in addition ordinary, then S^{0}(X, \omega_{X}) \neq 0 .

L’Enseignement Mathématique
École Polytechnique Fédérale de Lausanne (CH)
Openalex Percentile: Top 89%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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