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