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

Part of: Surfaces and higher-dimensional varieties (Co)homology theory Theory of modules and ideals General commutative ring theory

Published online by Cambridge University Press:  05 March 2013

Zsolt Patakfalvi  and
Karl Schwede
Zsolt Patakfalvi
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ, 08542, USA (pzs@princeton.edu)
Karl Schwede
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA (schwede@math.psu.edu)
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Abstract

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.

Keywords

depthCohen–MacaulayF-singularitiesbase changerelative canonical sheaf

MSC classification

Secondary: 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure 14J10: Families, moduli, classification 14J17: Singularities 14F18: Multiplier ideals 13C14: Cohen-Macaulay modules 13C15: Dimension theory, depth, related rings (catenary, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 1 , January 2014 , pp. 43 - 63
Copyright
©Cambridge University Press 2013 

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