Christian Liedtke

Title: Good Reduction of K3 surfaces

Abstract:
By a classical theorem of Serre and Tate, extending previous results of Néron, Ogg, 
and Shafarevich, an Abelian variety over the field of fractions K of a local 
Henselian DVR has good reduction if and only if the Galois action on its first 
l-adic cohomology is unramified (“no monodromy”). In this talk, we show that 
if the Galois action on second l-adic cohomology of a K3 surface over K is unramified, 
then the surface has admits an ``RDP model'', and good reduction (that is, 
a smooth model) after a finite and unramified extension. 
(Standing assumption: potential semi-stable reduction.) Moreover, we give examples 
where such an unramified extension is really needed. 
This is joint work with Yuya Matsumoto.