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 CohenMacaulay or at least has depth $\geq 3$ 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 arXiv:
 arXiv:1207.1910
 Bibcode:
 2012arXiv1207.1910P
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra;
 13A35;
 14J10;
 14J17;
 14F18;
 13C14;
 13C15
 EPrint:
 18 pages, typos corrected, exposition improved, Corollary 3.3 added. To appear in Journal of the Institute of Mathematics of Jussieu