## The minimal model program in characteristic p

### Edited by org.aimpl.user:johnl@math.mit.edu

This workshop, sponsored by AIM and the NSF, was devoted to the minimal model program in characteristic $p$.

Despite recent progress in characteristic zero in all dimensions relatively little is known about the birational geometry of varieties in characteristic $p$, even for threefolds. Kawamata-Viehweg vanishing is one of the central results in characteristic zero but unfortunately it is known that Kodaira vanishing fails even for surfaces in characteristic $p$.

The singularities which appear in the minimal model program are adapted to the use of Kawamata-Viehweg vanishing. In characteristic $p$ there are some closely related singularities which arise naturally when considering the action of Frobenius. One aim of the workshop was to understand how the two types of singularities compare.

Using ideas and techniques from characteristic zero coupled with some recent progress on alternatives to Kawamata-Viehweg vanishing in characteristic $p$, which use the action of Frobenius, one of the aims of the workshop was to attack problems in the birational geometry of threefolds and possibly even higher dimensions in characteristic $p$.

The main topics of the workshop were:

1. Vanishing theorems in finite characteristic.

2. The cone and base point free theorem in characteristic $p$.

3. Existence of three fold flips in characteristic $p$.

4. Semi-stable reduction for surfaces in characteristic $p$.

5. Boundedness of birational maps for threefolds.

6. The behavior of nef divisors modulo reduction to characteristic $p$.

Despite recent progress in characteristic zero in all dimensions relatively little is known about the birational geometry of varieties in characteristic $p$, even for threefolds. Kawamata-Viehweg vanishing is one of the central results in characteristic zero but unfortunately it is known that Kodaira vanishing fails even for surfaces in characteristic $p$.

The singularities which appear in the minimal model program are adapted to the use of Kawamata-Viehweg vanishing. In characteristic $p$ there are some closely related singularities which arise naturally when considering the action of Frobenius. One aim of the workshop was to understand how the two types of singularities compare.

Using ideas and techniques from characteristic zero coupled with some recent progress on alternatives to Kawamata-Viehweg vanishing in characteristic $p$, which use the action of Frobenius, one of the aims of the workshop was to attack problems in the birational geometry of threefolds and possibly even higher dimensions in characteristic $p$.

The main topics of the workshop were:

1. Vanishing theorems in finite characteristic.

2. The cone and base point free theorem in characteristic $p$.

3. Existence of three fold flips in characteristic $p$.

4. Semi-stable reduction for surfaces in characteristic $p$.

5. Boundedness of birational maps for threefolds.

6. The behavior of nef divisors modulo reduction to characteristic $p$.

### Sections

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