Abstract
We will prove the following results for -fold pairs over an algebraically closed field of characteristic : log flips exist for $\Q$-factorial dlt pairs ; log minimal models exist for projective klt pairs with pseudo-effective ; the log canonical ring is finitely generated for projective klt pairs when is a big $\Q$-divisor; semi-ampleness holds for a nef and big $\Q$-divisor if is nef and big and is projective klt; $\Q$-factorial dlt models exist for lc pairs ; terminal models exist for klt pairs ; ACC holds for lc thresholds; etc.
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