
## 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

#### 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

#### 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

#### 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.