Algebraic Geometry Seminar

Date, time & place Tuesday 15:30 - 17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

2015/05/25

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Yuya Matsumoto (University of Tokyo)
Good reduction of K3 surfaces (日本語 or English)
[ Abstract ]
We consider degeneration of K3 surfaces over a 1-dimensional base scheme
of mixed characteristic (e.g. Spec of the p-adic integers).
Under the assumption of potential semistable reduction, we first prove
that a trivial monodromy action on the l-adic etale cohomology group
implies potential good reduction, where potential means that we allow a
finite base extension.
Moreover we show that a finite etale base change suffices.
The proof for the first part involves a mixed characteristic
3-dimensional MMP (Kawamata) and the classification of semistable
degeneration of K3 surfaces (Kulikov, Persson--Pinkham, Nakkajima).
For the second part, we consider flops and descent arguments. This is a joint work with Christian Liedtke.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~ymatsu/index_j.html