# The minimal model program in characteristic p

April 29 to May 3, 2013

at the

American Institute of Mathematics, Palo Alto, California

organized by

James McKernan and Chenyang Xu

This workshop, sponsored by AIM and the NSF, will be 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 will be 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 will be to attack problems in the birational geometry of threefolds and possibly even higher dimensions in characteristic $p$.

The main topics of the workshop are

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 $p$.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.