The paper proves an equivalence between Cartier crystals and V-crystals on dual abelian varieties and derives H^0(X,ω_X)≠0, with S^0(X,ω_X)≠0 in the ordinary case, for normal proper varieties of maximal Albanese dimension.
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Generic vanishing theory in positive characteristic
The paper proves an equivalence between Cartier crystals and V-crystals on dual abelian varieties and derives H^0(X,ω_X)≠0, with S^0(X,ω_X)≠0 in the ordinary case, for normal proper varieties of maximal Albanese dimension.