Number Theory Seminar

Seminar information archive ~12/07Next seminarFuture seminars 12/08~

Date, time & place Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Naoki Imai, Shane Kelly

2010/10/06

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
Hélène Esnault (Universität Duisburg-Essen)
Finite group actions on the affine space (ENGLISH)
[ Abstract ]
If $G$ is a finite $\\ell$-group acting on an affine space $\\A^n$ over a
finite field $K$ of cardinality prime to $\\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\\ell$ divides $q-1$. To this aim, we study group actions on weak
N\\'eron models.
(Joint work with Johannes Nicaise)