The paper defines characteristic-zero liftings of positive-characteristic ideals via skeletons and proves discreteness of log discrepancies for smooth surface-multi-ideal pairs, plus containment of minimal log discrepancies and log canonical thresholds from positive characteristic inside the zero-1.
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Liftings of ideals in positive characteristic to those in characteristic zero:Surface case
The paper defines characteristic-zero liftings of positive-characteristic ideals via skeletons and proves discreteness of log discrepancies for smooth surface-multi-ideal pairs, plus containment of minimal log discrepancies and log canonical thresholds from positive characteristic inside the zero-1.