A Grauert-Riemenschneider vanishing theorem for Witt canonical sheaves

2025/06/17 by Jefferson Baudin, Baudin, Jefferson · 3 citations
Mathematics · #14F17 #14F30 #14G17 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F17 #msc:14F30 #msc:14G17

paper · pdf · doi:10.48550/arxiv.2506.14647

Final version. To appear in Inventiones Mathematicae

arxiv created 2026/07/29 · arxiv updated 2026/07/30

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 Rülling. We then deduce some rationality consequences for F-rational singularities.

Citations

• On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
• Quasi-F-splittings in birational geometry III
• Terminal 3-folds that are not Cohen-Macaulay
• Duality for Hodge-Witt cohomology with modulus
• The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails
• Applications of perverse sheaves in commutative algebra
• Duality between Cartier crystals and perverse \mathbbF_p-sheaves, and application to generic vanishing
• Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic p
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• On the relative Minimal Model Program for threefolds in low\n characteristics
• Kollár's injectivity theorem for globally F-regular varieties
• A Riemann-Hilbert correspondence in positive characteristic
• Vanishing theorems of Kodaira type for Witt canonical sheaves
• Rational points on log Fano threefolds over a finite field
• Projectivity of the Witt vector affine Grassmannian
• Generic vanishing in characteristic p>0 and the characterization of ordinary abelian varieties
• Langlands correspondence for isocrystals and the existence of crystalline companions for curves
• Theory of weights in p-adic cohomology
• Generic vanishing fails for singular varieties and in characteristic p>0
• Hodge-Witt cohomology and Witt-rational singularities
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• Higher direct images of the structure sheaf in positive characteristic
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Cited by

• On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
• On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
• On Gorenstein ℚ_p-rational threefold and fourfold singularities
• Duality between W_n-Cartier crystals and ℤ/pⁿℤ-perverse sheaves

Related

• Grauert-Riemenschneider Vanishing via modulus sheaves with transfers
• The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails
• Vanishing and a counterexample for Witt divisorial sheaves
• Vanishing theorems for threefolds in characteristic p>5
• On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type