Many problems in algebraic geometry can be solved by"reduction to characteristic p". This is a powerfultechnique, useful even when the primary objects of studyare complex algebraic varieties. It is also a beautifuland accessible example of the the utility of "scheme theory"in concrete problems about varieties.
The goal of this talk will be to introduce the noviceto the technique of reduction to characteristic p,and to discuss the special nature of varieties in charcacteristicp that makes them easier to handle. I'll also discusswhat kind of theorems one can expect to prove by this technique,and give some examples of recent theorems proved this way.
The talk is intended for graduate students and non-specialists inalgebraic geometry.