Date:
-
Location:
POT 745
Speaker(s) / Presenter(s):
Andrew Obus
TITLE: The Oort conjecture and its generalizations.
ABSTRACT: A common mathematical problem is to be given a mathematical object in
characteristic p, and to ask whether it is the reduction, in some
sense, of an analogous structure in characteristic zero. If so, the
structure in characteristic zero is called a "lift" of the structure
in characteristic p.
We will consider a power series version of this problem, called the "local lifting problem." Given a characteristic p algebraically closed field k, and an action of a finite group G on k[[t]] by k-automorphisms, is there a DVR R in characteristic zero with residue field k such that the action of G lifts to R[[t]]? Oort conjectured that this is true when G is cyclic, and this conjecture was proven by the speaker, Stefan Wewers, and Florian Pop. We will discuss this conjecture and its generalizations. Examples will be given throughout.
We remark that the motivation for studying the local lifting problem comes from understanding lifts of branched covers of curves from characteristic p to characteristic zero.