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Depth of $F$-singularities and base change of relative canonical sheaves

Published online by Cambridge University Press:  05 March 2013

Zsolt Patakfalvi
Department of Mathematics, Princeton University, Princeton, NJ, 08542, USA (
Karl Schwede
Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA (


For a characteristic-$p\gt 0$ variety $X$ with controlled $F$-singularities, we state conditions which imply that a divisorial sheaf is Cohen–Macaulay or at least has depth $\geq $3 at certain points. This mirrors results of Kollár for varieties in characteristic 0. As an application, we show that relative canonical sheaves are compatible with arbitrary base change for certain families with sharply $F$-pure fibers.

Research Article
©Cambridge University Press 2013 

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