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1. Fundamental MMP theorems

Analogs of the fundamentals theorems of the MMP in characteristic 0 whose positive characteristic forms remain open.

    1. Basepoint free theorem


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      Problem 1.1.

      [Tanaka] Suppose that k = \bar{k}, \text{char } k = p > 0. Let X/k be a terminal threefold, and A an ample \mathbb Q-divisor on X. If K_X+A is nef, must it be semiample?
          This is known in a couple cases: 1. X smooth, \nu(K_X+A) = 0.

      2. k = \bar{\mathbb F}_p, \dim X = 3, K_X+A big.

        • Termination in dimension 3


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          Problem 1.2.

          Do klt flips terminate in dimension 3?
              This is probably OK for terminal varieties, with the proof as in characteristic 0.

            • Connectedness


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              Problem 1.3.

              Is there a positive-characteristic analog of the connectedness lemma?

                  Cite this as: AimPL: The minimal model program in characteristic p, available at http://aimpl.org/minimalmodcharp.