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Arvidsson, Emelie; Bernasconi, Fabio; Lacini, Justin (, Compositio Mathematica)We prove the Kawamata–Viehweg vanishing theorem for surfaces of del Pezzo type over perfect fields of positive characteristic $p>5$ . As a consequence, we show that klt threefold singularities over a perfect base field of characteristic $p>5$ are rational. We show that these theorems are sharp by providing counterexamples in characteristic $$5$$ .more » « less
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Bernasconi, Fabio; Kollár, János (, International Mathematics Research Notices)Abstract We prove Grauert–Riemenschneider–type vanishing theorems for excellent divisiorally log terminal threefolds pairs whose closed points have perfect residue fields of positive characteristic $p>5$. Then we discuss applications to dlt singularities and to Mori fiber spaces of three-folds.more » « less
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