# Christopher Lazda: A Néron–Ogg–Shafarevich criterion for K3 surfaces

**Time: **
Wed 2018-12-12 13.15

**Lecturer: **
Christopher Lazda (University of Amsterdam)

**Location: ** Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Abstract: The naive analogue of the Néron–Ogg–Shafarevich criterion fails for K3 surfaces, that is, there exist K3 surfaces over Henselian, discretely valued fields *K*, with unramified étale cohomology groups, but which do not admit good reduction over *K*. Assuming potential semi-stable reduction, I will show how to correct this by proving that a K3 surface has good reduction if and only if its second cohomology is unramified, and the associated Galois representation over the residue field coincides with the second cohomology of a certain “canonical reduction” of *X*. This is joint work with B. Chiarellotto and C. Liedtke.