Trevor Arnold

Introduction to characteristic p methods in complex geometry

We attempt to sketch a general philosophy for reducing questions about complex varieties to varieties over finite fields. This method first involves finding a ``model'' for the complex situation over some finitely-generated Z-algebra A. Characteristic p results can then be applied to the fibers over the closed points of A. The second step is then to show that properties of these fibers are inherited by the generic fiber, thereby proving something about the original setup.