Modul:   MAT770  Oberseminar: Algebraische Geometrie

Rational fixed points for finite group actions, and a question of Serre

Talk by Dr. Johannes Nicaise

Speaker invited by: Prof. Dr. Joseph Ayoub

Date: 23.05.11  Time: 13.15 - 14.45  Room: Y27H25

Serre asked if the action of a finite $\ell$-group on an affine space over a field of characteristic different from $\ell$ always admits a rational fixed point. We will give a brief survey of known results and techniques, and we will show how one can use Loeser and Sebag's motivic Serre invariant to answer the question affirmatively if the base field is a henselian discretely valued field of characteristic zero with algebraically closed residue field of characteristic different from $\ell$. This is joint work with Hélène Esnault.