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Depth of
$F$-singularities and base change of relative canonical sheaves
- Part of
-
- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 13 / Issue 1 / January 2014
- Published online by Cambridge University Press:
- 05 March 2013, pp. 43-63
- Print publication:
- January 2014
-
- Article
- Export citation
-
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.
