K_{X/T} is pseudo-effective when f: X→T has non-uniruled generic fiber in char p>0.
Esnault : Varieties over a finite field with trivial C how group of 0-cycles have a rational point , Invent
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Pseudo-effectivity of the relative canonical divisor and uniruledness in positive characteristic
K_{X/T} is pseudo-effective when f: X→T has non-uniruled generic fiber in char p>0.