Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Depth of $F$-singularities and base change of relative canonical sheaves   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 $\geq 3$ at certain points. This mirrors results of Koll\'ar
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.

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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph