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A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves

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arxiv 2506.14647 v2 pith:SFTYYE4W submitted 2025-06-17 math.AG

Jefferson Baudin This is my paper · ORCID
classification math.AG
keywords grauert-riemenschneidertheoremvanishingwittblicklecanonicalcharacteristicchatzistamatiaou
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abstract

We prove a Witt vector version of the usual Grauert-Riemenschneider vanishing theorem over fields of positive characteristic, solving a question raised by Blickle, Esnault, Chatzistamatiaou and R\"ulling. We then deduce some rationality consequences for $F$-rational singularities.

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Cited by 2 Pith papers

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  1. On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension

    math.AG 2025-07 conditional novelty 7.0 of 10

    Smooth proper weakly ordinary varieties of maximal Albanese dimension satisfy chi(X, omega_X) >= 0, with chi = 0 for non-general-type examples and the Albanese image then fibered by ordinary abelian varieties.

  2. On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type

    math.AG 2025-06 conditional novelty 7.0 of 10

    The paper proves degree-one Grauert-Riemenschneider vanishing for Cohen-Macaulay klt-type schemes and, in dimension three, full GR vanishing and rational singularities.

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