The lifting problem we will consider roughly asks: given a smooth, proper, geometrically connected curve X in characteristic p with an action of a finite group G, does there exist a smooth, proper curve X' with G-action in characteristic zero such that X' (with G-action) lifts X (with G-action)? It turns out that solving this lifting problem reduces to solving a local lifting problem in a formal neighborhood of each point of X where G acts with non-trivial inertia. The Oort conjecture states that this local lifting problem should be solvable whenever the inertia group is cyclic. A new result of Stefan Wewers and the speaker shows that the local lifting problem is solvable whenever the inertia group is cyclic of order not divisible by p4, and in many cases even when the inertia group is cyclic and arbitrarily large. We will discuss this result, after giving a good amount of background on the local lifting problem in general. The talk should be of interest to people in algebraic geometry as well as number theory.
Freitag, den 16. Dezember 2011 um 13:30 Uhr, in INF 288, HS2 Freitag, den 16. Dezember 2011 at 13:30, in INF 288, HS2
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Dr. A. Holschbach