On the Birational Nature of Lifting
Christian Liedtke (Bonn)  Seminar Algebraic Geometry (SAG)
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When 
Jun 14, 2012 from 11:00 am to 12:15 pm 
Where  Bonn, Seminarraum MPI, Vivatsgasse 7 
Contact Name  sachinid 
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Whenever a variety X lifts from characteristic p to characteristic zero, say over the Witt ring, then many classical results over the complex numbers hold for X, and certain "characteristic p pathologies" cannot occur, simply because one can reduce modulo p (I will discuss this in examples). But then, lifting results are difficult, and generally, varieties do not lift. However, in many situations, it is possible or easier to lift a birational model of X, maybe even one that has "mild" singularities (again, I will give examples). So, a natural question is whether the liftability of such a birational model implies that of our original X. We will show that this completely fails in dimension at least 3, that this question is surprisingly subtle in dimension 2, and that it is trivial in dimension 1. This is joint work with Matthew Satriano.