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

Abstract

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

18 pages, typos corrected, exposition improved, Corollary 3.3 added. To appear in Journal of the Institute of Mathematics of Jussieu

References in corpus (2)

• Introduction to the log minimal model program for log canonical pairs
• Hulls and Husks

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